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We introduce a method to construct wave packets with complete classical and quantum correspondence in one-dimensional non-relativistic quantum mechanics. First, we consider two similar oscillators with equal total energy. In classical domain, we can easily solve this model and obtain the trajectories in the space of variables. This picture in the quantum level is equivalent with a hyperbolic partial differential equation which gives us a freedom for choosing the initial wave function and its initial slope. By taking advantage of this freedom, we propose a method to choose an appropriate initial condition which is independent from the form of the oscillators. We then construct the wave packets for some cases and show that these wave packets closely follow the whole classical trajectories and peak on them. Moreover, we use de-Broglie Bohm interpretation of quantum mechanics to quantify this correspondence and show that the resulting Bohmian trajectories are also in a complete agreement with their classical counterparts.

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.

Wave Mechanics Union specializes in big band and small ensemble arrangements of progressive and classic rock tunes.  Arranger and band member Ryan Fraley explains the process,  and we listen to versions of "Swordfishtrombone" by Tom Waits, "Elephant Talk" by King Crimson and "Wondrous Stories" by Yes.

The explanation of the first-order Stark effect in hydrogen by Epstein and Schwarzschild in 1916 was seen as a great success for the old quantum theory. Yet, it also revealed some serious limitations of the theory. To recover the experimentally found line splittings, one had to make some arbitrary assumptions in addition to the basic quantum conditions to rule out certain orbits. The calculation of intensities of lines on the basis of Bohr's correspondence principle likewise required arbitrary additional assumptions. Finally, the actual orbits predicted by the old quantum theory depend on the coordinates chosen to impose the quantum conditions. Both Sommerfeld and Epstein recognized this problem but offered no solution for it. All these problems were solved in 1926 when Schr\"odinger and Epstein explained the Stark effect on the basis of the new wave mechanics. The calculations in the two theories are similar. In particular, both the Schr\"odinger equation in the new theory and the Hamilton-Jacobi equation in the old theory are separated in parabolic coordinates. The new quantum mechanics determines all allowed states and transitions without any additional assumptions. It also replaced the ambiguous guidelines based on the correspondence principle for calculating intensities by the straightforward prescription that intensities are given by the squares of the matrix elements of position, leading to results that agreed much better with the experimental data. Finally, the embarrassing non-uniqueness of orbits in the old quantum theory turned into the innocuous non-uniqueness of bases of eigenfunctions in wave mechanics. To this day, the Stark effect is remembered as one of the few qualified successes of the old quantum theory. We suspect that this is largely because after 1926 it became just one of the many unqualified successes of the new quantum theory.

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.

pdf Equations from Book 1 Wave Mechanics of SM358 The Quantum World by The SM358 Course Team [2009] {530.12--oclc}

pdf Equations from Book 1 Wave Mechanics of SM358 The Quantum World by The SM358 Course Team [2009] {530.12--oclc}

Book Source: Digital Library of India Item 2015.211600 dc.contributor.author: Schrodinger,e dc.date.accessioned: 2015-07-09T17:35:19Z dc.date.available: 2015-07-09T17:35:19Z dc.date.digitalpublicationdate: 2004-11-15 dc.date.citation: 1908 dc.identifier.barcode: 1040010080295 dc.identifier.origpath: /data_copy/upload/0080/300 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/211600 dc.description.scannerno: 4 dc.description.scanningcentre: IISc, Bangalore dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 161 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Svinfo dc.publisher: Blackie And Son Limited dc.source.library: Jrd Tata Library,indian Institute Of Science,bangalore dc.subject.classification: Natural Sciences dc.subject.classification: Physics dc.subject.classification: General Mechanics. Mechanics Of Solid And Rigid Bodies dc.subject.keywords: Wave Mechanics dc.title: Collected Papers On Wave Mechanics

Recently I proposed the linguistic interpretation of quantum mechanics, which is characterized as the linguistic turn of the Copenhagen interpretation of quantum mechanics. This turn from physics to language does not only extend quantum theory to classical theory but also yield the quantum mechanical world view. Although the wave function collapse is prohibited in the linguistic interpretation, in this paper I show that the phenomenon like wave function collapse can be realized in the linguistic interpretation. And furthermore, I propose the justification of the von Neumann-L\"uders projection postulate. After all, I conclude that the wave function collapse should not be adopted in the Copenhagen interpretation.

We have recently constructed a photon position operator with commuting components. This was long thought to be impossible, but our position eigenvectors have a vortex structure like twisted light. Thus they are not spherically symmetric and the position operator does not transform as a vector, so that previous non-existence arguments do not apply. We find two classes of position eigenvectors and obtain photon wave functions by projection onto the bases of position eigenkets that they define, following the usual rules of quantum mechanics. The hermitian position operator, r0, leads to a Landau-Peierls wave function, while field-like eigenvectors of the nonhermitian position operator and its adjoint lead to a biorthonormal basis. These two bases are equivalent in the sense that they are related by a similarity transformation. The eigenvectors of the nonhermitian position operators lead to a field-potential wave function pair. These field-like positive frequency wave functions satisfy Maxwell's equations, and thus justify the supposition that MEs describe single photon wave mechanics. The expectation value of the number operator is photon density with undetected photons integrated over, consistent with Feynman's conclusion that the density of non-interacting particles can be interpreted as probability density.

We outline how Bohmian mechanics works: how it deals with various issues in the foundations of quantum mechanics and how it is related to the usual quantum formalism. We then turn to some objections to Bohmian mechanics, for example the fact that in Bohmian mechanics there is no back action of particle configurations upon wave functions. These lead us to our main concern: a more careful consideration of the meaning of the wave function in quantum mechanics, as suggested by a Bohmian perspective. We propose that the reason, on the universal level, that there is no action of configurations upon wave functions, as there seems to be between all other elements of physical reality, is that the wave function of the universe is not an element of physical reality. We propose that the wave function belongs to an altogether different category of existence than that of substantive physical entities, and that its existence is nomological rather than material. We propose, in other words, that the wave function is a component of physical law rather than of the reality described by the law.

This review covers applications of quantum Monte Carlo methods to quantum mechanical problems in the study of electronic and atomic structure, as well as applications to statistical mechanical problems both of static and dynamic nature. The common thread in all these applications is optimization of many-parameter trial states, which is done by minimization of the variance of the local or, more generally for arbitrary eigenvalue problems, minimization of the variance of the configurational eigenvalue.

This review covers applications of quantum Monte Carlo methods to quantum mechanical problems in the study of electronic and atomic structure, as well as applications to statistical mechanical problems both of static and dynamic nature. The common thread in all these applications is optimization of many-parameter trial states, which is done by minimization of the variance of the local or, more generally for arbitrary eigenvalue problems, minimization of the variance of the configurational eigenvalue.

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.

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.

Thermodynamic equivalence between classical many-body system and some auxiliary nonlinear auxiliary field is proved. Connection between Hamiltonians of the many-body system and the auxiliary field is derived.

Thermodynamic equivalence between classical many-body system and some auxiliary nonlinear auxiliary field is proved. Connection between Hamiltonians of the many-body system and the auxiliary field is derived.

This paper studies the propagation of weakly nonlinear waves. The analysis is applicable to plasma waves, surface water waves, the interaction of laser beams with matter, particle accelerators, etc. The specific motivation for this work is, however, the study of internal waves in the ocean. Hamilton's principle is used to write the fluid equations in Hamiltonian form in terms of linear eigenmode amplitudes. Numerical studies are made of the effect of Fourier grid size and resonance widths. Statistical information is generated from an ensemble of initial states of the random wave field. (Author)

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.

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.

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 2015.220691 dc.contributor.author: Schrodinger. E dc.date.accessioned: 2015-07-09T21:50:18Z dc.date.available: 2015-07-09T21:50:18Z dc.date.digitalpublicationdate: 2005-05-18 dc.date.citation: 1928 dc.identifier.barcode: 2990140053783 dc.identifier.origpath: /data_copy/upload/0053/788 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/220691 dc.description.scannerno: 7 dc.description.scanningcentre: Osmania University dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 172 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Digital Library Of India dc.publisher: Blackie And Son Limited dc.rights: Not Available dc.source.library: Osmania University dc.subject.classification: Natural Sciences dc.subject.classification: Physics dc.subject.classification: Vibratrions. Acoustics dc.title: Collected Papers On Wave Mechanics

Book Source: Digital Library of India Item 2015.220691 dc.contributor.author: Schrodinger. E dc.date.accessioned: 2015-07-09T21:50:18Z dc.date.available: 2015-07-09T21:50:18Z dc.date.digitalpublicationdate: 2005-05-18 dc.date.citation: 1928 dc.identifier.barcode: 2990140053783 dc.identifier.origpath: /data_copy/upload/0053/788 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/220691 dc.description.scannerno: 7 dc.description.scanningcentre: Osmania University dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 172 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Digital Library Of India dc.publisher: Blackie And Son Limited dc.rights: Not Available dc.source.library: Osmania University dc.subject.classification: Natural Sciences dc.subject.classification: Physics dc.subject.classification: Vibratrions. Acoustics dc.title: Collected Papers On Wave Mechanics

Book Source: Digital Library of India Item 2015.163860 dc.contributor.author: Louis De Broglie And Leon Brillouin dc.contributor.other: Indian Institute Of Science dc.date.accessioned: 2015-07-06T23:12:00Z dc.date.available: 2015-07-06T23:12:00Z dc.date.digitalpublicationdate: 0000-00-00 dc.date.citation: 1928 dc.identifier.barcode: 1010010032032 dc.identifier.origpath: /data/upload/0032/037 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/163860 dc.description.scanningcentre: IISc, Bangalore dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 160 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Vishwas dc.publisher: Blackie And Son Limited dc.rights: Out_of_copyright dc.source.library: Iisc Library dc.subject.classification: Physics dc.title: Selected Papers On Wave Mechanics

A series of numerical simulations of ground response to a high- explosive detonation was used to examine the influence of material models on calculated central-peak formation in shock-produced craters. One simulation of the 20-ton high-explosive detonation Mixed Company II showed that computed motions at 16.4 msec. when ballistically extrapolated, were consistent with the observed crater and formation of a central mound. Compaction, layering, and material yield models were varied in additional simulations. The results indicated the occurrence of a central mound is primarily dependent on material properties of the medium.

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

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

viii, 193 p. illus. ; 20 cm

Low-energy quasiparticle states, arising from scattering by single-particle potentials in d-wave superconductors, are addressed. Via a natural extension of the Andreev approximation, the idea that sign-variations in the superconducting pair-potential lead to such states is extended beyond its original setting of boundary scattering to the broader context of scattering by general single-particle potentials, such as those due to impurities. The index-theoretic origin of these states is exhibited via a simple connection with Witten's supersymmetric quantum-mechanical model.

"Unabridged and corrected version of the first edition [1951]"

"Unabridged and corrected version of the first edition [1951]"

Until recently, wave-particle duality has been thought of as quantum principle without a counterpart in classical physics. This belief was challenged after (i) finding that average dynamics of a classical particle in strong inhomogeneous oscillating field resembles that of a quantum object and (ii) experimental discovery of "walkers" - macroscopic droplets that bounce on a vertically vibrating bath of the same fluid and can self-propell via interaction with the surface waves they generate. This paper exposes a new family of objects that can display both particle and wave features all together while strictly obeying laws of the Newtonian mechanics. In contrast to the previously known duality examples in classical physics, oscillating field or constant inflow of energy are not required for their existence. These objects behave deterministically provided that all their degrees of freedom are known to an observer. If, however, some degrees of freedom are unknown, observer can describe such objects only {\it probabilistically} and they manifest {\it weird} features similar to that of quantum particles. We show new classical counterparts of such quantum phenomena as particle interference, tunneling, above-barrier reflection, trapping on top of a barrier, and spontaneous emission of radiation. In the light of these findings, we hypothesize that quantum mechanics may \emph{emerge} as approximation from a more profound theory on a deeper level.

Until recently, wave-particle duality has been thought of as quantum principle without a counterpart in classical physics. This belief was challenged after (i) finding that average dynamics of a classical particle in strong inhomogeneous oscillating field resembles that of a quantum object and (ii) experimental discovery of "walkers" - macroscopic droplets that bounce on a vertically vibrating bath of the same fluid and can self-propell via interaction with the surface waves they generate. This paper exposes a new family of objects that can display both particle and wave features all together while strictly obeying laws of the Newtonian mechanics. In contrast to the previously known duality examples in classical physics, oscillating field or constant inflow of energy are not required for their existence. These objects behave deterministically provided that all their degrees of freedom are known to an observer. If, however, some degrees of freedom are unknown, observer can describe such objects only {\it probabilistically} and they manifest {\it weird} features similar to that of quantum particles. We show new classical counterparts of such quantum phenomena as particle interference, tunneling, above-barrier reflection, trapping on top of a barrier, and spontaneous emission of radiation. In the light of these findings, we hypothesize that quantum mechanics may \emph{emerge} as approximation from a more profound theory on a deeper level.

255 pages ; 30 cm

255 pages ; 30 cm

255 pages ; 30 cm

255 pages ; 30 cm

A dynamical, non-Euclidean spacetime geometry in general relativity theory implies the possibility of gravitational radiation. Here we explore novel methods of detecting such radiation from astrophysical sources by means of matter-wave interferometers (MIGOs), using atomic beams emanating from supersonic atomic sources that are further cooled and collimated by means of optical molasses. While the sensitivities of such MIGOs compare favorably with LIGO and LISA, the sizes of MIGOs can be orders of magnitude smaller, and their bandwidths wider. Using a pedagogical approach, we place this problem into the broader context of problems at the intersection of quantum mechanics with general relativity.

In 1929 Lanczos showed how to derive Dirac's equation from a more fundamental system that predicted that spin 1/2 particles should come in pairs. Today, these pairs can unambiguously be interpreted as isospin doublets. From the same fundamental equation, Lanczos derived also the correct form of the wave equation of massive spin 1 particles that would be rediscovered in 1936 by Proca. Lanczos's fundamental system was put in Lagrangian form and generalized in 1933 by Einstein and Mayer, who used the semivector instead of the quaternion formalism. Although they not did study all possible solutions, Einstein and Mayer showed that the doublets consisted of particles with different mass and charge. In fact, there are two main classes of doublets: proton/neutron and electron/neutrino pairs.

Wave mechanics of a particle in 1-D box (size $= d$) is critically analyzed to reveal its untouched aspects. When the particle rests in its ground state, its zero-point force ($F_o$) produces non-zero strain by modifying the box size from $d$ to $d' = d + \Delta d$ in all practical situations where the force ($F_a$) restoring $d$ is not infinitely strong. Assuming that $F_a$ originates from a potential $\propto x^2$ ($x$ being a small change in $d$), we find that: (i) the particle and strained box assume a mutually bound state (under the equilibrium between $F_o$ and $F_a$) with binding energy $\Delta{E} = -\epsilon_o'\Delta{d}/d'$ (with $\epsilon_o' = h^2/8md'^2$ being the ground state energy of the particle in the strained box), (ii) the box size oscillates around $d'$ when the said equilibrium is disturbed, (iii) an exchange of energy between the particle and the strained box occurs during such oscillations, and (iv) the particle, having collisional motion in its excited states, assumes collisionless motion in its ground state. These aspects have desired experimental support and proven relevance for understanding the physics of widely different systems such as quantum dots, quantum wires, trapped single particle/ion, clusters of particles, superconductors, superfluids, {\it etc.} It is emphasized that the physics of such a system in its low energy states can be truly revealed if the theory incorporates $F_o$ and related aspects.

The response of a plane Poiseuille flow to disturbances of various initial wavenumbers and amplitudes is investigated by numerically integrating the equation of motion. It is shown that for very low amplitude disturbances the numerical integration scheme yields results that are consistent with those predictable from linear theory. It is also shown that because of non-linear interactions a growing unstable disturbance excites higher wavenumber modes which have the same frequency, or phase velocity, as the primary mode. For very low amplitude disturbances these spontaneously generated higher wavenumber modes have a strong resemblance to certain modes computed from the linear Orr-Sommerfeld equation. In general it is found that the disturbance is dominated for a long time by the primary mode and that there is little alteration of the original parabolic mean velocity profile. There is evidence of the existence of an energy equilibrium state which is common to all finite-amplitude disturbances despite their initial wavenumbers. This equilibrium energy level is roughly 3-5% of the energy in the mean flow which is an order of magnitude higher than the equilibrium value predicted by existing non-linear theories.

The response of a plane Poiseuille flow to disturbances of various initial wavenumbers and amplitudes is investigated by numerically integrating the equation of motion. It is shown that for very low amplitude disturbances the numerical integration scheme yields results that are consistent with those predictable from linear theory. It is also shown that because of non-linear interactions a growing unstable disturbance excites higher wavenumber modes which have the same frequency, or phase velocity, as the primary mode. For very low amplitude disturbances these spontaneously generated higher wavenumber modes have a strong resemblance to certain modes computed from the linear Orr-Sommerfeld equation. In general it is found that the disturbance is dominated for a long time by the primary mode and that there is little alteration of the original parabolic mean velocity profile. There is evidence of the existence of an energy equilibrium state which is common to all finite-amplitude disturbances despite their initial wavenumbers. This equilibrium energy level is roughly 3-5% of the energy in the mean flow which is an order of magnitude higher than the equilibrium value predicted by existing non-linear theories.

According to Schroedinger's ideas, classical dynamics of point particles should correspond to the " geometrical optics " limit of a linear wave equation, in the same way as ray optics is the limit of wave optics. It is shown that, using notions of modern wave theory, the " geometrical optics " analogy leads to the correspondence between a classical Hamiltonian H and a " quantum " wave equation in a natural and general way. In particular, the correspondence is unambiguous also in the case where H contains mixed terms involving momentum and position. In the line of Schroedinger's ideas, it is also attempted to justify the occurrence, in QM, of eigenvalues problems, not merely for energy, but also for momentum. It is shown that the wave functions of pure momentum states can be defined in a physically more satisfying way than by assuming plane waves. In the case of a spatially uniform force field, such momentum states have a singularity and move undeformed according to Newton's second law. The mentioned unambiguous correspondence allows to uniquely extend the Klein-Gordon relativistic wave equation to the case where a constant gravitational field is present. It is argued that Schroedinger's wave mechanics can be extended to the case with a variable gravitational field only if one accepts that the wave equation is a preferred-frame one. From this viewpoint, generally-covariant extensions of the wave equations of QM seem rather formal. Finally, it is conjectured that there is no need for a quantum gravity.

The propagation of waves through microstructured media with periodically arranged inclusions has applications in many areas of physics and engineering, stretching from photonic crystals through to seismic metamaterials. In the high-frequency regime, modelling such behaviour is complicated by multiple scattering of the resulting short waves between the inclusions. Our aim is to develop an asymptotic theory for modelling systems with arbitrarily-shaped inclusions located on general Bravais lattices. We then consider the limit of point-like inclusions, the advantage being that exact solutions can be obtained using Fourier methods, and go on to derive effective medium equations using asymptotic analysis. This approach allows us to explore the underlying reasons for dynamic anisotropy, localisation of waves, and other properties typical of such systems, and in particular their dependence upon geometry. Solutions of the effective medium equations are compared with the exact solutions, shedding further light on the underlying physics. We focus on examples that exhibit dynamic anisotropy as these demonstrate the capability of the asymptotic theory to pick up detailed qualitative and quantitative features.

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.

We derive the spectra of D=2, SU(3) supersymmetric Yang-Mills quantum mechanics in all fermionic sectors. Moreover, we provide exact expressions for the corresponding eigenvectors in the sectors with none and one fermionic quantum. We also generalize our results obtained in a cut Fock space to the infinite cut-off limit.

We derive the spectra of D=2, SU(3) supersymmetric Yang-Mills quantum mechanics in all fermionic sectors. Moreover, we provide exact expressions for the corresponding eigenvectors in the sectors with none and one fermionic quantum. We also generalize our results obtained in a cut Fock space to the infinite cut-off limit.