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The probability operator is derived from first principles for an equilibrium quantum system. It is also shown that the superposition states collapse into a mixture of states giving the conventional von Neumann trace form for the quantum average. The mechanism for the collapse is found to be quite general: it results from the conservation law for a conserved, exchangeable variable (such as energy) and the entanglement of the total system wave function that necessarily follows. The relevance of the present results to the einselection mechanism for decoherence, to the quantum measurement problem, and to the classical nature of the macroscopic world are discussed.

THE present volume forming the second Part of my Wave Mechanics is devoted (as foreshadowed in the Preface to Part I) to the mathematical development of the general ideas underlying the new mechanics, connecting it with classical mechanics and constituting it a complete self-supporting theory. In building up the mathematical framework of this theory I have limited myself to what I consider its most essential elements, leaving aside a number of questions which have a methodological value only (such as the group theory) or which are met with in the solution of special problems. I t is my intention to consider some of these questions later on in connexion with the special problems which will be discussed in Part III (Advanced Special Theory’) ; I have carefully avoided complicating the general scheme of the theory by such special questions—with a few exceptions inserted for illustration (the relativistic theory of the hydrogen-like atom, for example). To make the general scheme more comprehensible I have not spared space, dealing with especially important general questions (such as the transformation and the perturbation theory, or the relativistic theory of the electron) at much greater length than would be necessary from the point of view of an adequate presentation to a sophisticated reader. I must cordially thank the editors for their readiness to meet my demands on space, which have resulted in a book larger than was originally contemplated. I must also thank M. L. Urquhart and Miss B. Swirles for help in correcting the English and the proofs. The present book, like Part I, is complete in itself, and can be read without acquaintance with Part I, provided the reader is familiar with some elementary account of wave mechanics, and is ready to explore its mathematical depths to obtain a profounder insight into the theory and to prepare himself for applying it to various special problems. The earlier portions of this book were written in 1931 while I was in America; it was completed in Leningrad nearly two years later. Some of the shortcomings of the book are due to this interruption and the impossibility of revising it in 1933 from the very beginning. A list of the more important references for each section is given at the end of the book; it is followed by a short index which should enable the reader to locate easily all the more important subjects treated.

The application of the elements of quantum (wave) mechanics to some special problems in the field of macroscopic fluid dynamics is discussed. Emphasis is placed on the flow of a viscous, incompressible fluid around a circular cylinder. The following subjects are considered: (1) the flow of a nonviscous fluid around a circular cylinder, (2) the restrictions imposed the stream function by the number of dimensions of space, and (3) the flow past three dimensional bodies in a viscous fluid, particularly past a circular cylinder in the symmetrical case.

The application of the elements of quantum (wave) mechanics to some special problems in the field of macroscopic fluid dynamics is discussed. Emphasis is placed on the flow of a viscous, incompressible fluid around a circular cylinder. The following subjects are considered: (1) the flow of a nonviscous fluid around a circular cylinder, (2) the restrictions imposed the stream function by the number of dimensions of space, and (3) the flow past three dimensional bodies in a viscous fluid, particularly past a circular cylinder in the symmetrical case.

xiv, 401 p. 24 cm

The application of the basic formalistic elements of wave mechanics theory is discussed. The theory is used to describe the physical phenomena on the microscopic level, the fluid dynamics of gases and liquids, and the analysis of physical phenomena on the macroscopic (visually observable) level. The practical advantages of relating the two fields of wave mechanics and fluid mechanics through the use of the Schroedinger equation constitute the approach to this relationship. Some of the subjects include: (1) fundamental aspects of wave mechanics theory, (2) laminarity of flow, (3) velocity potential, (4) disturbances in fluids, (5) introductory elements of the bifurcation theory, and (6) physiological aspects in fluid dynamics.

The application of the basic formalistic elements of wave mechanics theory is discussed. The theory is used to describe the physical phenomena on the microscopic level, the fluid dynamics of gases and liquids, and the analysis of physical phenomena on the macroscopic (visually observable) level. The practical advantages of relating the two fields of wave mechanics and fluid mechanics through the use of the Schroedinger equation constitute the approach to this relationship. Some of the subjects include: (1) fundamental aspects of wave mechanics theory, (2) laminarity of flow, (3) velocity potential, (4) disturbances in fluids, (5) introductory elements of the bifurcation theory, and (6) physiological aspects in fluid dynamics.

The application of the basic formalistic elements of wave mechanics theory is discussed. The theory is used to describe the physical phenomena on the microscopic level, the fluid dynamics of gases and liquids, and the analysis of physical phenomena on the macroscopic (visually observable) level. The practical advantages of relating the two fields of wave mechanics and fluid mechanics through the use of the Schroedinger equation constitute the approach to this relationship. Some of the subjects include: (1) fundamental aspects of wave mechanics theory, (2) laminarity of flow, (3) velocity potential, (4) disturbances in fluids, (5) introductory elements of the bifurcation theory, and (6) physiological aspects in fluid dynamics.

The fundamental impasses and ruptures in various domains of the canonical, unitary science, or the 'end of science', become the more and more evident. The natural unity of being is recovered within a universal nonperturbative method leading to the dynamic redundance paradigm. It is shown that the unreduced behaviour of any nontrivial (isolated) system includes many equally real, but incompatible dynamic regimes, each of them being roughly equivalent to an ordinary 'complete' solution of the unitary science. Therefore the regimes should 'spontaneously' and randomly replace one another, which provides a universal, purely dynamic origin of randomness. The discovered dynamic redundance leads to the universal, reality-based concept of dynamic complexity and its permanently developing hierarchical structure, alias the world. Its lowest levels give the causally complete mechanics of dynamically quantized elementary fields, extending the double solution found by Louis de Broglie. One obtains a physically complete solution for the 'mysteries' of quantum mechanics, unifyng it with the extended, causal versions of relativity (emergent space and time), quantum and classical gravity (dynamical mass), field theory (electric charge and spin), particle physics, and cosmology. The same key features of the unreduced dynamic complexity determine behaviour of any system at higher levels of complexity described by a case of the single, universal equation in its two related versions, the extended Lagrange-Hamilton (trajectorial) and Schroedinger (distributional) equations. The end of the unitary science opens the renaissance of the ultimately complete and universal understanding initiated by Rene Descartes (but then mechanistically falsified), which is confirmed by many sound, practically important results.

We consider the problem of an atomic beam propagating quantum mechanically through an atom beam splitter. Casting the problem in an adiabatic representation (in the spirit of the Born-Oppenheimer approximation in molecular physics) sheds light on explicit effects due to non-adiabatic passage of the atoms through the splitter region. We are thus able to probe the fully three dimensional structure of the beam splitter, gathering quantitative information about mode-mixing, splitting ratios,and reflection and transmission probabilities.

We extend our previous analysis of the motion of vortex lines [I. Bialynicki-Birula, Z. Bialynicka-Birula and C. Sliwa, Phys. Rev. A 61, 032110 (2000)] from linear to a nonlinear Schroedinger equation with harmonic forces. We also argue that under certain conditions the influence of the contact nonlinearity on the motion of vortex lines is negligible. The present analysis adds new weight to our previous conjecture that the topological features of vortex dynamics are to a large extent universal.

A new quantum mechanical description of the dynamics of wave packet under continuous measurement is formulated via Bohmian mechanics. The solution to this equation is found through a wave packet approach which establishes a direct correlation between a classical variable with a quantum variable describing the dynamics of the center of mass and the width of the wave packet. The approach presented in this paper gives a comparatively clearer picture than approaches using restrited path integrals and master equation approaches. This work shows how the extremely irregular character of classical chaos can be reconciled with the smooth and wavelike nature of phenomena on the atomic scale. It is demonstrated that a wave packet under continuous quantum measurement displays both chaotic and non-chaotic features. The Lyapunov characteristic exponents for the trajectories of classical particle and the quantum wave packet center of mass are calculated and their chaoticities are demonstrated to be about the same. Nonetheless, the width of the wave packet exhibits a non-chaotic behavior and allows for the possibility to beat the standard quantum limit by means of transient, contractive states.

It is well known that a state with complex energy cannot be the eigenstate of a self-adjoint operator, like the Hamiltonian. Resonances, i.e. states with exponentially decaying observables, are not vectors belonging to the conventional Hilbert space. One can describe these resonances in an unusual mathematical formalism, based on the so-called Rigged Hilbert Space (RHS). In the RHS, the states with complex energy are denoted as Gamow Vectors (GV), and they model decay processes. We study GV of the Reversed Harmonic Oscillator (RHO), and we analytically and numerically investigate the unstable evolution of wave packets. We introduce the background function to study initial data not composed only by a summation of GV and we analyse different wave packets belonging to specific function spaces. Our work furnishes support to the idea that irreversible wave propagations can be investigated by means of Rigged Hilbert Space Quantum Mechanics and provides insights for the experimental investigation of irreversible dynamics.

Source: Digital Library of India Scanning Centre: IISc, Bangalore Source Library: Jrd Tata Library,indian Institute Of Science,bangalore Date Accessioned: 7/9/2015 19:44 The Digital Library of India was a project under the auspices of the Government of India.

Source: Digital Library of India Scanning Centre: IISc, Bangalore Source Library: Jrd Tata Library,indian Institute Of Science,bangalore Date Accessioned: 7/9/2015 19:44 The Digital Library of India was a project under the auspices of the Government of India.

An investigation of inverse problems as basic problems in science, in which physical systems are to be identified on the basis of experimental observations. These problems are especially important in astrophysics and astronomy, for their objects of investigation are frequently not observable in a direct fashion. Solar and stellar structure, for example, is estimated from the study of spectra, while the structure of a planetary atmosphere may be deducted from measurements of reflected sunlight. This memorandum shows that a wide class of inverse problems may now be solved with high-speed computers and modern computational techniques.

This paper appeared in a collection of papers titled "Scientific Papers Presented to Max Born on his retirement from the Tait Chair of Natural Philosophy in the University of Edinburgh", published in 1953 (Oliver and Boyd).

This paper appeared in a collection of papers titled "Scientific Papers Presented to Max Born on his retirement from the Tait Chair of Natural Philosophy in the University of Edinburgh", published in 1953 (Oliver and Boyd).

We calculate a tunneling time distribution by means of Nelson's quantum mechanics and investigate its statistical properties. The relationship between the average and deviation of tunneling time suggests the exsistence of ``wave-particle duality'' in the tunneling phenomena.

The Cellular Automata (CA) method is based on the idea that the macroscopic behavior of a system can be captured by using simple local rules running at a microscopic level. In other words, a system can be modeled by means of simple local rules that govern the behavior of the whole system. In this thesis a local CA rule set is introduced and a methodology is developed to model physical systems that are governed by one and two dimensional wave equations. One dimensional systems are also successfully modeled by using CA and FEM techniques working as coupled, whereas two dimensional systems could only be modeled in an error margin due to the variation of the introduced time scaling factor when external forces are involved. Also, the applicability of the CA method to fracture mechanics problems is investigated.

Book Source: Digital Library of India Item 2015.177623 dc.date.accessioned: 2015-07-07T05:23:53Z dc.date.available: 2015-07-07T05:23:53Z dc.date.digitalpublicationdate: 0000-00-00 dc.date.citation: 1929 dc.identifier.barcode: 99999990013703 dc.identifier.origpath: /data/upload/0013/708 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/177623 dc.description.scanningcentre: IIAp, Bangalore dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 149 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Iiap dc.publisher: Methuen And Company dc.rights: Out_of_copyright dc.source.library: Indian Institute Of Astrophysics dc.title: Wave Mechanics dc.rights.holder: Methuen And Company

High-speed photography has been used to observe and define the pattern of stresses generated by an explosive charge detonated on the end of a right circular cylinder. It was found that the internally convex cylindrical surface transforms and focuses the energy of the blow first in the form of a converging tensile wave which is followed shortly by a similarly converging shear wave. Damage is successively wrought by the two converging waves which arrive one after the other; the damage being due to the shear wave extending further down the cylinder. The diameter of the cylinder regulates the extent of the damage, limiting severe damage to the first three diameters of length. Within another diameter or so of length, the original dilatational wave is essentially transformed into a rod wave.

High-speed photography has been used to observe and define the pattern of stresses generated by an explosive charge detonated on the end of a right circular cylinder. It was found that the internally convex cylindrical surface transforms and focuses the energy of the blow first in the form of a converging tensile wave which is followed shortly by a similarly converging shear wave. Damage is successively wrought by the two converging waves which arrive one after the other; the damage being due to the shear wave extending further down the cylinder. The diameter of the cylinder regulates the extent of the damage, limiting severe damage to the first three diameters of length. Within another diameter or so of length, the original dilatational wave is essentially transformed into a rod wave.

High-speed photography has been used to observe and define the pattern of stresses generated by an explosive charge detonated on the end of a right circular cylinder. It was found that the internally convex cylindrical surface transforms and focuses the energy of the blow first in the form of a converging tensile wave which is followed shortly by a similarly converging shear wave. Damage is successively wrought by the two converging waves which arrive one after the other; the damage being due to the shear wave extending further down the cylinder. The diameter of the cylinder regulates the extent of the damage, limiting severe damage to the first three diameters of length. Within another diameter or so of length, the original dilatational wave is essentially transformed into a rod wave.

Using the concept of intercepting orbits from a pair of Space Station serviced free flyers, a class of impact and shock wave experiments pertinent to planetary science can be performed. One proposed free flying vehicle is an impactor dispensor, and the second is the impact laboratory. How collision is achieved by utilizing essentially twice orbital velocity is demonstrated. The impactor dispensor contains a series of small flyer plates or other projectiles which are launched into the trajectory of the impactor laboratory at appropriate positions. The impactor laboratory is a large impact tank similar to those in terrestrial gun laboratories, except that it contains a supply of targets and instrumentation such as high speed cameras, flash X-ray apparatus, and digital recorders. Shock and isentropic pressures of up to 20 Mbar are achievable with such a system which provides 15 km/sec impact velocities for precisely oriented projectiles.

Book Source: Digital Library of India Item 2015.77754 dc.contributor.author: Broglie,louis De dc.contributor.author: Flint,h.t. dc.date.accessioned: 2015-06-30T16:03:30Z dc.date.available: 2015-06-30T16:03:30Z dc.date.digitalpublicationdate: 2005-04-27 dc.date.citation: 1930 dc.identifier.barcode: 2030020005685 dc.identifier.origpath: /data7/upload/0185/121 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/77754 dc.description.scannerno: 2 dc.description.scanningcentre: RMSC, IIIT-H dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 275 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Digital Library Of India dc.publisher: Methuen And Co.ltd. dc.rights: In_copyright dc.source.library: Osmania University dc.subject.classification: Natural Sciences dc.subject.classification: Physics dc.title: An Introduction To The Study Of Wave Mechanics

Book Source: Digital Library of India Item 2015.77754 dc.contributor.author: Broglie,louis De dc.contributor.author: Flint,h.t. dc.date.accessioned: 2015-06-30T16:03:30Z dc.date.available: 2015-06-30T16:03:30Z dc.date.digitalpublicationdate: 2005-04-27 dc.date.citation: 1930 dc.identifier.barcode: 2030020005685 dc.identifier.origpath: /data7/upload/0185/121 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/77754 dc.description.scannerno: 2 dc.description.scanningcentre: RMSC, IIIT-H dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 275 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Digital Library Of India dc.publisher: Methuen And Co.ltd. dc.rights: In_copyright dc.source.library: Osmania University dc.subject.classification: Natural Sciences dc.subject.classification: Physics dc.title: An Introduction To The Study Of Wave Mechanics

Scan of book Quantum mechanics of particles and wave fields by Arthur March b18910223 d19570417 [1951] {531--loc} Chapter titles: Wave Mechanics of a Single Particle;  Wave Mechanics of Stationary States; Wave Mechanics in Matrix Form; Perturbation Theory; Systems of Many Particles; Relativistic Wave Equations; Quantization of Wave Fields; Quantum Electrodynamics; Wave Fields and Nuclear Matter; Introduction of a Fundamental Length

Using exact solutions, we show that it is in principle possible to regard waves and particles as representations of the same underlying geometry, thereby resolving the problem of wave-particle duality.

We consider a one-dimensional partial differential equation system modeling heat flow around a ring. The system includes a Klein-Gordon wave equation for a field satisfying spatial periodic boundary conditions, as well as Ornstein-Uhlenbeck stochastic differential equations with finite rank dissipation and stochastic driving terms modeling heat baths. There is an energy flow around the ring. In the case of a linear field with different (fixed) bath temperatures, the energy flow can persist even when the interaction with the baths is turned off. A simple example is given.

Hilbert space combines the properties of two fundamentally different types of mathematical spaces: vector space and metric space. While the vector-space aspects of Hilbert space, such as formation of linear combinations of state vectors, are routinely used in quantum mechanics, the metric-space aspects of Hilbert space are much less exploited. Here we show that a suitable metric stratifies Fock space into concentric spheres. Maximum and minimum distances between wave functions are derived and geometrically interpreted in terms of this metric. Unlike the usual Hilbert-space analysis, our results apply also to the reduced space of only ground-state wave functions and to that of particle densities, each of which forms a metric space but not a Hilbert space. The Hohenberg-Kohn mapping between densities and ground-state wave functions, which is highly complex and nonlocal in coordinate description, is found, for three different model systems, to be very simple in metric space, where it is represented by a monotonic mapping of vicinities onto vicinities. Surprisingly, it is also found to be nearly linear over a wide range of parameters.

255 pages ; 30 cm

-classical mechanics as the limiting form of wave mechanics; operators; matrices; transformation theory; perturbation theory; relativistic remodeling and magnetic generalization of the wave mechanics of a single electron; the problem of many particles; reduction of the problem of a system of identical particles to that of a single particle; second quantization and quantum electrodynamics-

Theory of remaining energy —wave mechanics of particles in curved space-time(Part III) 作者： Yu Xianqiao 1 作者单位： 1. School of Physical Science and Technology, Southwest University, Chongqing 400715, China 通讯作者： Yu Xianqiao Email:[email protected] 提交时间： 2023-03-25 摘要: In this article, based on the wave equation established in the first part of this series, I have studied the evolution of the energy density of the universe from the initial moment to the present, and found that there is still residual energy of the initial energy of the universe, which appears in the form of vacuum energy. The residual energy is the simplest explanation for dark matter. The calculations show that the present average energy of each momentum mode in the residual energy is of the order of 10^{-3} eV, which is approximately 3 to 5 times the averaged energy of photons in the cosmic microwave background. residual energy dark matter 来自： 余先桥 分类： 物理学 >> 普通物理:统计和量子力学,量子信息等 物理学 >> 地球物理学、天文学和天体物理学 说明： 这篇文章是关于弯曲时空中粒子的波动力学系列论文（共3篇）中的第三篇。This article is the thirdin a series of papers (3 in total) on wave mechanics of particles in curved space-time.这篇文章同时也是ChinaXiv:202101.00003 的补充完善。 投稿状态： 未投稿 引用： ChinaXiv:202303.08731 (或此版本 ChinaXiv:202303.08731V1 ) DOI:10.12074/202303.08731V1 CSTR:32003.36.ChinaXiv.202303.08731.V1 推荐引用方式： Yu Xianqiao.(2023).Theory of remaining energy —wave mechanics of particles in curved space-time(Part III).中国科学院科技论文预发布平台.doi:10.12074/202303.08731V1 版本历史 [V1] 2023-03-25 11:16:14 ChinaXiv:202303.08731V1 下载全文

This paper proves a locality principle for a wave-mechanical particle governed by the Schroedinger equation. It is shown that rho(r,Beta), the Laplace transform of the local density of states n(r,E), depends significantly only on the potential V(r') at points r' near r. The effect of changes of V(r') at distant points r' (abs. val. (r' - r) d) on rho(r,Beta), decay in a Gaussian fashion with a. This result sheds some light on the locality of physical properties of extended systems and provides general support for various local methods of calculation. (Author)

It has been long known that a year after Schrödinger published his equation, Madelung also published a hydrodynamics version of Schrödinger equation. Quantum diffusion is studied via dissipative Madelung hydrodynamics. Initially the wave packet spreads ballistically, than passes for an instant through normal diffusion and later tends asymptotically to a sub‐diffusive law. In this paper we will review two different approaches, including Madelung hydrodynamics and also Bohm potential. Madelung formulation leads to diffusion interpretation, which after a generalization yields to Ermakov equation. Since Ermakov equation cannot be solved analytically, then we try to find out its solution with Mathematica package. It is our hope that these methods can be verified and compared with experimental data. But we admit that more researches are needed to fill all the missing details.

We consider the classical limit of quantum mechanics in terms of Bohmian trajectories. For wave packets as defined by Hagedorn we show that the Bohmian trajectories converge to Newtonian trajectories in probability.

The development of mathematically complete and consistent models solving the so-called "measurement problem", strongly renewed the interest of the scientific community for the foundations of quantum mechanics, among these the Dynamical Reduction Models posses the unique characteristic to be experimentally testable. In the first part of the paper an upper limit on the reduction rate parameter of such models will be obtained, based on the analysis of the X-ray spectrum emitted by an isolated slab of germanium and measured by the IGEX experiment. The second part of the paper is devoted to present the results of the VIP (Violation of the Pauli exclusion principle) experiment and to describe its recent upgrade. The VIP experiment established a limit on the probability that the Pauli Exclusion Principle (PEP) is violated by electrons, using the very clean method of searching for PEP forbidden atomic transitions in copper.

We present our model of an Emergent Quantum Mechanics which can be characterized by "realism without pre-determination". This is illustrated by our analytic description and corresponding computer simulations of Bohmian-like "surreal" trajectories, which are obtained classically, i.e. without the use of any quantum mechanical tool such as wave functions. However, these trajectories do not necessarily represent ontological paths of particles but rather mappings of the probability density flux in a hydrodynamical sense. Modelling emergent quantum mechanics in a high-low intesity double slit scenario gives rise to the "quantum sweeper effect" with a characteristic intensity pattern. This phenomenon should be experimentally testable via weak measurement techniques.

An expansion for quantum statistical mechanics is derived that gives classical statistical mechanics as the leading term. Each quantum correction comes from successively larger permutation loops, which arise from the factorization of the symmetrization of the wave function with respect to localized particle interchange. Explicit application of the theory yields the full fugacity expansion for the quantum ideal gas, and the second fugacity coefficient for interacting quantum particles, which agree with known results. Compared to the Lee-Yang virial cluster expansion, the present expansion is expected to be more rapidly converging and the individual terms appear to be simpler to evaluate. The results obtained in this paper are intended for practical computer simulation algorithms for terrestrial condensed matter quantum systems.

I review the basic ``gravitational instability'' model for the growth of structure in the expanding Universe. This model requires the existence of small initial irregularities in the density of a largely uniform universe. These grow through linear and non-linear stages to form a complex network of clusters, filaments and voids. The dynamical equations describing the evolution of a self-gravitating fluid can be rewritten in the form of a Schrodinger equation coupled to a Poisson equation determining the gravitational potential. This approach has a number of interesting features, many of which were pointed out in a seminal paper by Widrow & Kaiser (1993). I argue that this approach has the potential to yield useful analytic insights into the dynamical growth of large-scale structure. As a particular example, I show that this approach yields an elegant reformulation of an idea due to Jones (1999) concerning the origin of lognormal intermittency in the galaxy distribution.

Source: Digital Library of India Scanning Centre: C-DAC, Noida Source Library: Central Library, Bits- Pilani Date Accessioned: 9/23/2015 15:51 The Digital Library of India was a project under the auspices of the Government of India.

Source: Digital Library of India Scanning Centre: C-DAC, Noida Source Library: Central Library, Bits- Pilani Date Accessioned: 9/23/2015 15:51 The Digital Library of India was a project under the auspices of the Government of India.

The tomographic invertable map of the Wigner function onto the positive probability distribution function is studied. Alternatives to the Schr\"odinger evolution equation and to the energy level equation written for the positive probability distribution are discussed. Instead of the transition probability amplitude (Feynman path integral) a transition probability is introduced. A new formulation of the conventional quantum mechanics (without wave function and density matrix) based on the ``probability representation'' of quantum states is given. An equation for the propagator in the new formulation of quantum mechanics is derived. Some paradoxes of quantum mechanics are reconsidered.

The dynamical equations describing the evolution of a self-gravitating fluid of cold dark matter (CDM) can be written in the form of a Schrodinger equation coupled to a Poisson equation describing Newtonian gravity. It has recently been shown that, in the quasi-linear regime, the Schrodinger equation can be reduced to the exactly solvable free-particle Schrodinger equation. The free-particle Schrodinger equation forms the basis of a new approximation scheme -the free-particle approximation - that is capable of evolving cosmological density perturbations into the quasi-linear regime. The free-particle approximation is essentially an alternative to the adhesion model in which the artificial viscosity term in Burgers' equation is replaced by a non-linear term known as the quantum pressure. Simple one-dimensional tests of the free-particle method have yielded encouraging results. In this paper we comprehensively test the free-particle approximation in a more cosmologically relevant scenario by appealing to an N-body simulation. We compare our results with those obtained from two established methods: the linearized fluid approach and the Zeldovich approximation. We find that the free-particle approximation comprehensively out-performs both of these approximation schemes in all tests carried out and thus provides another useful analytical tool for studying structure formation on cosmological scales.

We consider a toy model of pointer interacting with a 1/2-spin system, whose $\sigma_{x}$ variable is \emph{measured} by the environment, according to the prescription of decoherence theory. If the environment measuring the variable $\sigma_{x}$ yields ordinary statistical mechanics, the pointer sensitive to the 1/2-spin system undergoes the same, exponential, relaxation regardless of whether real collapses or an entanglement with the environment, mimicking the effect of real collapses, occur. In the case of non-ordinary statistical mechanics the occurrence of real collapses make the pointer still relax exponentially in time, while the equivalent picture in terms of reduced density matrix generates an inverse power law relaxation.

We consider a toy model of pointer interacting with a 1/2-spin system, whose $\sigma_{x}$ variable is \emph{measured} by the environment, according to the prescription of decoherence theory. If the environment measuring the variable $\sigma_{x}$ yields ordinary statistical mechanics, the pointer sensitive to the 1/2-spin system undergoes the same, exponential, relaxation regardless of whether real collapses or an entanglement with the environment, mimicking the effect of real collapses, occur. In the case of non-ordinary statistical mechanics the occurrence of real collapses make the pointer still relax exponentially in time, while the equivalent picture in terms of reduced density matrix generates an inverse power law relaxation.

The source of cosmological constant —wave mechanics of particles in curved space-time(Part II) 作者： Yu Xianqiao 1 作者单位： 1. School of Physical Science and Technology, Southwest University 通讯作者： Yu Xianqiao Email:[email protected] 提交时间： 2023-03-13 摘要: In this article, we will see that the existence of cosmological constant is a natural possible result of the new wave equation, which has been established in the first part of this series. After analyzing various possible sources of cosmological constant, the most likely conclusion is drawn that the cosmological constant is not from the vacuum energy of matter, but from space itself, it is an inherent essential feature of space itself. cosmological constant wave equation 来自： 余先桥 分类： 物理学 >> 普通物理:统计和量子力学,量子信息等 物理学 >> 地球物理学、天文学和天体物理学 说明： 这篇文章是关于弯曲时空中粒子的波动力学系列论文（共3篇）中的第二篇。This article is the second in a series of papers (3 in total) on wave mechanics of particles in curved space-time. 投稿状态： 未投稿 引用： ChinaXiv:202303.00133 (或此版本 ChinaXiv:202303.00133V1 ) doi:10.12074/202303.00133 CSTR:32003.36.ChinaXiv.202303.00133.V1 推荐引用方式： Yu Xianqiao.(2023).The source of cosmological constant —wave mechanics of particles in curved space-time(Part II).中国科学院科技论文预发布平台.[ChinaXiv:202303.00133] 版本历史 [V1] 2023-03-13 10:50:46 ChinaXiv:202303.00133V1 下载全文

Wave equation—wave mechanics of particles in curved space-time(Part I) 作者： Yu Xianqiao 1 作者单位： 1. School of Physical Science and Technology, Southwest University, Chongqing 400715, China 通讯作者： Yu Xianqiao Email:[email protected] 提交时间： 2023-03-13 摘要: In this paper, a universal wave equation of the motion of microscopic particles in curved space-time is established, which satisfies the conservation of probability. Under the classical limit conditions, the wave equation returns to the dynamic equation of special relativity. The application of the wave equation in the evolution of a flat expanding universe has preliminarily proved the correctness of the equation, and the new wave equation may open a window for us to understand physics within the Planck scale. wave equation curved space-time Planck scale 来自： 余先桥 分类： 物理学 >> 普通物理:统计和量子力学,量子信息等 说明： 这篇文章是关于弯曲时空中粒子的波动力学系列论文（共3篇）中的第一篇。This article is the first in a series of papers (3 in total) on wave mechanics of particles in curved space-time. 投稿状态： 未投稿 引用： ChinaXiv:202303.00003 (或此版本 ChinaXiv:202303.00003V2 ) DOI:10.12074/202303.00003V1 CSTR:32003.36.ChinaXiv.202303.00003.V2 推荐引用方式： Yu Xianqiao.(2023).Wave equation—wave mechanics of particles in curved space-time(Part I).中国科学院科技论文预发布平台.doi:10.12074/202303.00003V1 版本历史 [V2] 2023-03-13 10:31:38 ChinaXiv:202303.00003V2 下载全文

Wave equation—wave mechanics of particles in curved space-time(Part I) 作者： Yu Xianqiao 1 作者单位： 1. School of Physical Science and Technology, Southwest University, Chongqing 400715, China 通讯作者： Yu Xianqiao Email:[email protected] 提交时间： 2023-03-13 摘要: In this paper, a universal wave equation of the motion of microscopic particles in curved space-time is established, which satisfies the conservation of probability. Under the classical limit conditions, the wave equation returns to the dynamic equation of special relativity. The application of the wave equation in the evolution of a flat expanding universe has preliminarily proved the correctness of the equation, and the new wave equation may open a window for us to understand physics within the Planck scale. wave equation curved space-time Planck scale 来自： 余先桥 分类： 物理学 >> 普通物理:统计和量子力学,量子信息等 说明： 这篇文章是关于弯曲时空中粒子的波动力学系列论文（共3篇）中的第一篇。This article is the first in a series of papers (3 in total) on wave mechanics of particles in curved space-time. 投稿状态： 未投稿 引用： ChinaXiv:202303.00003 (或此版本 ChinaXiv:202303.00003V2 ) DOI:10.12074/202303.00003V1 CSTR:32003.36.ChinaXiv.202303.00003.V2 推荐引用方式： Yu Xianqiao.(2023).Wave equation—wave mechanics of particles in curved space-time(Part I).中国科学院科技论文预发布平台.doi:10.12074/202303.00003V1 版本历史 [V2] 2023-03-13 10:31:38 ChinaXiv:202303.00003V2 下载全文