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The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading the research literature in quantum computation and quantum information theory. This paper is a written version of the first of eight one hour lectures given in the American Mathematical Society (AMS) Short Course on Quantum Computation held in conjunction with the Annual Meeting of the AMS in Washington, DC, USA in January 2000, and will appear in the AMS PSAPM volume entitled "Quantum Computation." Part 1 of the paper is an introduction the to the concept of the qubit. Part 2 gives an introduction to quantum mechanics covering such topics as Dirac notation, quantum measurement, Heisenberg uncertainty, Schrodinger's equation, density operators, partial trace, multipartite quantum systems, the Heisenberg versus the Schrodinger picture, quantum entanglement, EPR paradox, quantum entropy. Part 3 gives a brief introduction to quantum computation, covering such topics as elementary quantum computing devices, wiring diagrams, the no-cloning theorem, quantum teleportation, Shor's algorithm, Grover's algorithm. Many examples are given. A table of contents as well as an index are provided for readers who wish to "pick and choose." Since this paper is intended for a diverse audience, it is written in an informal style at varying levels of difficulty and sophistication from the very elementary to the more advanced.

The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading the research literature in quantum computation and quantum information theory. This paper is a written version of the first of eight one hour lectures given in the American Mathematical Society (AMS) Short Course on Quantum Computation held in conjunction with the Annual Meeting of the AMS in Washington, DC, USA in January 2000, and will appear in the AMS PSAPM volume entitled "Quantum Computation." Part 1 of the paper is an introduction the to the concept of the qubit. Part 2 gives an introduction to quantum mechanics covering such topics as Dirac notation, quantum measurement, Heisenberg uncertainty, Schrodinger's equation, density operators, partial trace, multipartite quantum systems, the Heisenberg versus the Schrodinger picture, quantum entanglement, EPR paradox, quantum entropy. Part 3 gives a brief introduction to quantum computation, covering such topics as elementary quantum computing devices, wiring diagrams, the no-cloning theorem, quantum teleportation, Shor's algorithm, Grover's algorithm. Many examples are given. A table of contents as well as an index are provided for readers who wish to "pick and choose." Since this paper is intended for a diverse audience, it is written in an informal style at varying levels of difficulty and sophistication from the very elementary to the more advanced.

Starting from the famous Pauli problem on the possibility to associate quantum states with probabilities, the formulation of quantum mechanics in which quantum states are described by fair probability distributions (tomograms, i.e. tomographic probabilities) is reviewed in a pedagogical style. The relation between the quantum state description and the classical state description is elucidated. The difference of those sets of tomograms is described by inequalities equivalent to a complete set of uncertainty relations for the quantum domain and to nonnegativity of probability density on phase space in the classical domain. Intersection of such sets is studied. The mathematical mechanism which allows to construct different kinds of tomographic probabilities like symplectic tomograms, spin tomograms, photon number tomograms, etc., is clarified and a connection with abstract Hilbert space properties is established. Superposition rule and uncertainty relations in terms of probabilities as well as quantum basic equation like quantum evolution and energy spectra equations are given in explicit form. A method to check experimentally uncertainty relations is suggested using optical tomograms. Entanglement phenomena and the connection with semigroups acting on simplexes are studied in detail for spin states in the case of two qubits. The star-product formalism is associated with the tomographic probability formulation of quantum mechanics.

Starting from the famous Pauli problem on the possibility to associate quantum states with probabilities, the formulation of quantum mechanics in which quantum states are described by fair probability distributions (tomograms, i.e. tomographic probabilities) is reviewed in a pedagogical style. The relation between the quantum state description and the classical state description is elucidated. The difference of those sets of tomograms is described by inequalities equivalent to a complete set of uncertainty relations for the quantum domain and to nonnegativity of probability density on phase space in the classical domain. Intersection of such sets is studied. The mathematical mechanism which allows to construct different kinds of tomographic probabilities like symplectic tomograms, spin tomograms, photon number tomograms, etc., is clarified and a connection with abstract Hilbert space properties is established. Superposition rule and uncertainty relations in terms of probabilities as well as quantum basic equation like quantum evolution and energy spectra equations are given in explicit form. A method to check experimentally uncertainty relations is suggested using optical tomograms. Entanglement phenomena and the connection with semigroups acting on simplexes are studied in detail for spin states in the case of two qubits. The star-product formalism is associated with the tomographic probability formulation of quantum mechanics.

Starting from the famous Pauli problem on the possibility to associate quantum states with probabilities, the formulation of quantum mechanics in which quantum states are described by fair probability distributions (tomograms, i.e. tomographic probabilities) is reviewed in a pedagogical style. The relation between the quantum state description and the classical state description is elucidated. The difference of those sets of tomograms is described by inequalities equivalent to a complete set of uncertainty relations for the quantum domain and to nonnegativity of probability density on phase space in the classical domain. Intersection of such sets is studied. The mathematical mechanism which allows to construct different kinds of tomographic probabilities like symplectic tomograms, spin tomograms, photon number tomograms, etc., is clarified and a connection with abstract Hilbert space properties is established. Superposition rule and uncertainty relations in terms of probabilities as well as quantum basic equation like quantum evolution and energy spectra equations are given in explicit form. A method to check experimentally uncertainty relations is suggested using optical tomograms. Entanglement phenomena and the connection with semigroups acting on simplexes are studied in detail for spin states in the case of two qubits. The star-product formalism is associated with the tomographic probability formulation of quantum mechanics.

Book Source: Digital Library of India Item 2015.222769 dc.contributor.author: Pauling,linus. dc.contributor.author: Bright Wilson E. dc.date.accessioned: 2015-07-09T22:55:24Z dc.date.available: 2015-07-09T22:55:24Z dc.date.digitalpublicationdate: 2005-05-23 dc.date.citation: 1935 dc.identifier.barcode: 2990140053970 dc.identifier.origpath: /data_copy/upload/0053/975 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/222769 dc.description.scannerno: 3 dc.description.scanningcentre: Osmania University dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 479 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Digital Library Of India dc.publisher: Mcgraw Hill Book Company Inc. dc.rights: Copyright Permitted dc.source.library: Osmania University dc.subject.classification: Natural Sciences dc.subject.classification: Physics dc.subject.classification: General Mechanics. Mechanics Of Solid And Rigid Bodies dc.title: Introduction To Quantum Mechanics

Book Source: Digital Library of India Item 2015.222769 dc.contributor.author: Pauling,linus. dc.contributor.author: Bright Wilson E. dc.date.accessioned: 2015-07-09T22:55:24Z dc.date.available: 2015-07-09T22:55:24Z dc.date.digitalpublicationdate: 2005-05-23 dc.date.citation: 1935 dc.identifier.barcode: 2990140053970 dc.identifier.origpath: /data_copy/upload/0053/975 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/222769 dc.description.scannerno: 3 dc.description.scanningcentre: Osmania University dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 479 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Digital Library Of India dc.publisher: Mcgraw Hill Book Company Inc. dc.rights: Copyright Permitted dc.source.library: Osmania University dc.subject.classification: Natural Sciences dc.subject.classification: Physics dc.subject.classification: General Mechanics. Mechanics Of Solid And Rigid Bodies dc.title: Introduction To Quantum Mechanics

Book Source: Digital Library of India Item 2015.222769 dc.contributor.author: Pauling,linus. dc.contributor.author: Bright Wilson E. dc.date.accessioned: 2015-07-09T22:55:24Z dc.date.available: 2015-07-09T22:55:24Z dc.date.digitalpublicationdate: 2005-05-23 dc.date.citation: 1935 dc.identifier.barcode: 2990140053970 dc.identifier.origpath: /data_copy/upload/0053/975 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/222769 dc.description.scannerno: 3 dc.description.scanningcentre: Osmania University dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 479 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Digital Library Of India dc.publisher: Mcgraw Hill Book Company Inc. dc.rights: Copyright Permitted dc.source.library: Osmania University dc.subject.classification: Natural Sciences dc.subject.classification: Physics dc.subject.classification: General Mechanics. Mechanics Of Solid And Rigid Bodies dc.title: Introduction To Quantum Mechanics

This video provides a basic introduction to the Schrödinger equation by exploring how it can be used to perform simple quantum mechanical calculations. After explaining the basic structure of the equation, the infinite square well potential is used as a case study. The separation of variables approach is used to solve the Schrödinger equation and Born's probabilistic interpretation of the wave-function is used to calculate the expectation value of the position of a particle in a box. Stationary states are discussed, and it is shown that a linear superposition of energy eigenstates leads to non-stationary states with uncertain energy. The oscillation frequency of a simple superposition of states is calculated and comparisons with radiation emission from atoms is discussed. References: Quantum physics of atoms, molecules, solids, nuclei and particles - Eisberg and Resnick (Motivating the structure of the Schrodinger equation) Introduction to Quantum Mechanics - Griffiths and Schroeter (Examples of expectation values and superposition of states). Introduction to Quantum Mechanics - Phillips Vibrations and Waves - King The Quantum Story - Jim Baggot Quantum Physics for Dummies - Steven Holzner Thirty Years that Shook Physics - Gamow Inward Bound - Abraham Pais You can help support this channel via the Physics Explained Patreon account: https://www.patreon.com/physicsexplained You can follow me on instagram: https://www.instagram.com/physics_explained_ig You can follow me on Twitter: https://twitter.com/PhysicsExplain1

This video provides a basic introduction to the Schrödinger equation by exploring how it can be used to perform simple quantum mechanical calculations. After explaining the basic structure of the equation, the infinite square well potential is used as a case study. The separation of variables approach is used to solve the Schrödinger equation and Born's probabilistic interpretation of the wave-function is used to calculate the expectation value of the position of a particle in a box. Stationary states are discussed, and it is shown that a linear superposition of energy eigenstates leads to non-stationary states with uncertain energy. The oscillation frequency of a simple superposition of states is calculated and comparisons with radiation emission from atoms is discussed. References: Quantum physics of atoms, molecules, solids, nuclei and particles - Eisberg and Resnick (Motivating the structure of the Schrodinger equation) Introduction to Quantum Mechanics - Griffiths and Schroeter (Examples of expectation values and superposition of states). Introduction to Quantum Mechanics - Phillips Vibrations and Waves - King The Quantum Story - Jim Baggot Quantum Physics for Dummies - Steven Holzner Thirty Years that Shook Physics - Gamow Inward Bound - Abraham Pais You can help support this channel via the Physics Explained Patreon account: https://www.patreon.com/physicsexplained You can follow me on instagram: https://www.instagram.com/physics_explained_ig You can follow me on Twitter: https://twitter.com/PhysicsExplain1

This video provides a basic introduction to the Schrödinger equation by exploring how it can be used to perform simple quantum mechanical calculations. After explaining the basic structure of the equation, the infinite square well potential is used as a case study. The separation of variables approach is used to solve the Schrödinger equation and Born's probabilistic interpretation of the wave-function is used to calculate the expectation value of the position of a particle in a box. Stationary states are discussed, and it is shown that a linear superposition of energy eigenstates leads to non-stationary states with uncertain energy. The oscillation frequency of a simple superposition of states is calculated and comparisons with radiation emission from atoms is discussed. References: Quantum physics of atoms, molecules, solids, nuclei and particles - Eisberg and Resnick (Motivating the structure of the Schrodinger equation) Introduction to Quantum Mechanics - Griffiths and Schroeter (Examples of expectation values and superposition of states). Introduction to Quantum Mechanics - Phillips Vibrations and Waves - King The Quantum Story - Jim Baggot Quantum Physics for Dummies - Steven Holzner Thirty Years that Shook Physics - Gamow Inward Bound - Abraham Pais You can help support this channel via the Physics Explained Patreon account: https://www.patreon.com/physicsexplained You can follow me on instagram: https://www.instagram.com/physics_explained_ig You can follow me on Twitter: https://twitter.com/PhysicsExplain1

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Professor Pimentel emphasizes the advantages of the quantum mechanical model of the atom, as presented in the classroom film, over the planetary model. He discusses the relationship of quantum number to the spatial distribution of the electron in the one-electron atom. He then considers the screening effect of electrons at lower energy levels upon those at higher energy levels, and the relationship of the quantum states of the electrons to the periodic table.

a very berief and easy to follow guide to understanding of quantum mechanics

a very berief and easy to follow guide to understanding of quantum mechanics

a very berief and easy to follow guide to understanding of quantum mechanics

a very berief and easy to follow guide to understanding of quantum mechanics

a very berief and easy to follow guide to understanding of quantum mechanics

a very berief and easy to follow guide to understanding of quantum mechanics

a very berief and easy to follow guide to understanding of quantum mechanics

Volume 1 of this revised and updated edition provides an accessible and practical introduction to the first gauge theory included in the Standard Model of particle physics: quantum electrodynamics (QED).The book includes self-contained presentations of electromagnetism as a gauge theory as well as relativistic quantum mechanics. It provides a uniqu

Volume 1 of this revised and updated edition provides an accessible and practical introduction to the first gauge theory included in the Standard Model of particle physics: quantum electrodynamics (QED).The book includes self-contained presentations of electromagnetism as a gauge theory as well as relativistic quantum mechanics. It provides a uniqu

Volume 1 of this revised and updated edition provides an accessible and practical introduction to the first gauge theory included in the Standard Model of particle physics: quantum electrodynamics (QED).The book includes self-contained presentations of electromagnetism as a gauge theory as well as relativistic quantum mechanics. It provides a uniqu

From the Preface: "In this book, an attempt has been made to present quantum mechanics from the point of view of electrical engineers and to show that they are already familiar with many of the mathematical concepts and algebraic operations which are required.... This book frequently departs from the presentation common in introductory texts prepared for the use of physicists. The differences, however, are didactic, rather than of substance." Short, but surprisingly complete for its time (1967). Includes Schrodinger's time-independent and -dependent equations, Heisenberg's and Pauli's matrices and even a discussion on Dirac's relativistic equations. Uses analogies from the EE world like line-transmission theory. You'll see "j" used as the imaginary unit in all equations.

From the Preface: "In this book, an attempt has been made to present quantum mechanics from the point of view of electrical engineers and to show that they are already familiar with many of the mathematical concepts and algebraic operations which are required.... This book frequently departs from the presentation common in introductory texts prepared for the use of physicists. The differences, however, are didactic, rather than of substance." Short, but surprisingly complete for its time (1967). Includes Schrodinger's time-independent and -dependent equations, Heisenberg's and Pauli's matrices and even a discussion on Dirac's relativistic equations. Uses analogies from the EE world like line-transmission theory. You'll see "j" used as the imaginary unit in all equations.

Introduction to quantum mechanics. Overview of quantum physics, How is it different from Classical physics? , why do we need an interpretation here?  what does it say about reality? And some other speculations. Video originally derived from the Lighthouse  YouTube channel.

468 p. : 23 cm

369 p. 24 cm

369 p. 24 cm

-survey of classical mechanics; the old quantum theory; the schrödinger wave equation with the harmonic oscillator as an example; the wave equation for a system of point particles in three dimensions; the hydrogen atom; perturbation theory; the variation method and other approximate methods; the spinning electron and the pauli exclusion principle, with a discussion of the helium atom; many-electron atoms; the rotation and vibration of molecules; perturbation theory involving the time, the emission and absorption of radiation, and the resonance phenomenon; the structure of simple molecules; the structure of complex molecules; miscellaneous applications of quantum mechanics; general theory of quantum mechanics; appendixes-

-survey of classical mechanics; the old quantum theory; the schrödinger wave equation with the harmonic oscillator as an example; the wave equation for a system of point particles in three dimensions; the hydrogen atom; perturbation theory; the variation method and other approximate methods; the spinning electron and the pauli exclusion principle, with a discussion of the helium atom; many-electron atoms; the rotation and vibration of molecules; perturbation theory involving the time, the emission and absorption of radiation, and the resonance phenomenon; the structure of simple molecules; the structure of complex molecules; miscellaneous applications of quantum mechanics; general theory of quantum mechanics; appendixes-

-survey of classical mechanics; the old quantum theory; the schrödinger wave equation with the harmonic oscillator as an example; the wave equation for a system of point particles in three dimensions; the hydrogen atom; perturbation theory; the variation method and other approximate methods; the spinning electron and the pauli exclusion principle, with a discussion of the helium atom; many-electron atoms; the rotation and vibration of molecules; perturbation theory involving the time, the emission and absorption of radiation, and the resonance phenomenon; the structure of simple molecules; the structure of complex molecules; miscellaneous applications of quantum mechanics; general theory of quantum mechanics; appendixes-

By using the general concepts of special relativity and the requirements of quantum mechanics, Dirac equation is derived and studied. Only elementary knowledge of spin and rotations in quantum mechanics and standard handlings of linear algebra are employed for the development of the present work.

By using the general concepts of special relativity and the requirements of quantum mechanics, Dirac equation is derived and studied. Only elementary knowledge of spin and rotations in quantum mechanics and standard handlings of linear algebra are employed for the development of the present work.

By using the general concepts of special relativity and the requirements of quantum mechanics, Dirac equation is derived and studied. Only elementary knowledge of spin and rotations in quantum mechanics and standard handlings of linear algebra are employed for the development of the present work.

This document is the lecture script of a one-semester course taught at the University of Basel in the Fall semesters of 2012 and 2013 and in the Spring semester of 2015. It is aimed at advanced students of physics who are familiar with the concepts and notations of quantum mechanics. Quantum mechanics lectures can often be separated into two classes. In the first class you get to know Schroedinger's equation and find the form and dynamics of simple physical systems (square well, harmonic oscillator, hydrogen atom); most calculations are analytic and inspired by calculations originally done in the 1920s and 1930s. In the second class you learn about large systems such as molecular structures, crystalline solids, or lattice models; these calculations are usually so complicated that it is difficult for the student to understand them in all detail. This lecture tries to bridge the gap between simple analytic calculations and complicated large-scale computations. We will revisit most of the problems encountered in introductory quantum mechanics, focusing on computer implementations for finding analytical as well as numerical solutions and their visualization. Most of these calculations are too complicated to be done by hand. Even relatively simple problems, such as two interacting particles in a one-dimensional trap, do not have analytic solutions and require the use of computers for their solution and visualization. More complex problems scale exponentially with the number of degrees of freedom, and make the use of large computer simulations unavoidable. The course is taught using the Mathematica programming language; however, the concepts presented are readily translated to any other programming language.

This document is the lecture script of a one-semester course taught at the University of Basel in the Fall semesters of 2012 and 2013 and in the Spring semester of 2015. It is aimed at advanced students of physics who are familiar with the concepts and notations of quantum mechanics. Quantum mechanics lectures can often be separated into two classes. In the first class you get to know Schroedinger's equation and find the form and dynamics of simple physical systems (square well, harmonic oscillator, hydrogen atom); most calculations are analytic and inspired by calculations originally done in the 1920s and 1930s. In the second class you learn about large systems such as molecular structures, crystalline solids, or lattice models; these calculations are usually so complicated that it is difficult for the student to understand them in all detail. This lecture tries to bridge the gap between simple analytic calculations and complicated large-scale computations. We will revisit most of the problems encountered in introductory quantum mechanics, focusing on computer implementations for finding analytical as well as numerical solutions and their visualization. Most of these calculations are too complicated to be done by hand. Even relatively simple problems, such as two interacting particles in a one-dimensional trap, do not have analytic solutions and require the use of computers for their solution and visualization. More complex problems scale exponentially with the number of degrees of freedom, and make the use of large computer simulations unavoidable. The course is taught using the Mathematica programming language; however, the concepts presented are readily translated to any other programming language.

This document is the lecture script of a one-semester course taught at the University of Basel in the Fall semesters of 2012 and 2013 and in the Spring semester of 2015. It is aimed at advanced students of physics who are familiar with the concepts and notations of quantum mechanics. Quantum mechanics lectures can often be separated into two classes. In the first class you get to know Schroedinger's equation and find the form and dynamics of simple physical systems (square well, harmonic oscillator, hydrogen atom); most calculations are analytic and inspired by calculations originally done in the 1920s and 1930s. In the second class you learn about large systems such as molecular structures, crystalline solids, or lattice models; these calculations are usually so complicated that it is difficult for the student to understand them in all detail. This lecture tries to bridge the gap between simple analytic calculations and complicated large-scale computations. We will revisit most of the problems encountered in introductory quantum mechanics, focusing on computer implementations for finding analytical as well as numerical solutions and their visualization. Most of these calculations are too complicated to be done by hand. Even relatively simple problems, such as two interacting particles in a one-dimensional trap, do not have analytic solutions and require the use of computers for their solution and visualization. More complex problems scale exponentially with the number of degrees of freedom, and make the use of large computer simulations unavoidable. The course is taught using the Mathematica programming language; however, the concepts presented are readily translated to any other programming language.

Introduction to quamtum machanics

Introduction to quamtum machanics

There is a huge number of excellent and comprehensive textbooks on quantum mechanics. They mainly differ for the approach, more or less oriented to the formalism rather than to the phenomenology, as well as for the topics covered. These lectures have been based mainly on the classical textbook by Gasiorowicz (1974). I must confess that the main reason for my choice of Gasiorowicz (1974) is affective, as it was the textbook were I first learned the basic principles of quantum mechanics. Beyond my personal taste, I now recognize that Gasiorowicz (1974) is still a very good textbook on quantum mechanics, with a rigorous theoretical approach accompanied by a wide collection of applications. If the textbook by Gasiorowicz was my main basis, I have taken much also from other textbooks such as Phillips (2003), as well as from the excellent classical textbook by Dirac (1981).

The fifth edition of this well-established, highly regarded two-volume set continues to provide a fundamental introduction to advanced particle physics while incorporating substantial new experimental results, especially in the areas of Higgs and top sector physics, as well as CP violation and neutrino oscillations. It offers an accessible and practical introduction to the three gauge theories comprising the Standard Model of particle physics: quantum electrodynamics (QED), quantum chromodynamics (QCD), and the Glashow-Salam-Weinberg (GSW) electroweak theory. Volume 1 of this updated edition provides a broad introduction to the first of these theories, QED. The book begins with self-contained presentations of relativistic quantum mechanics and electromagnetism as a gauge theory. Lorentz transformations, discrete symmetries, and Majorana fermions are covered. A unique feature is the elementary introduction to quantum field theory, leading in easy stages to covariant perturbation theory and Feynman graphs, thereby establishing a firm foundation for the formal and conceptual framework upon which the subsequent development of the three quantum gauge field theories of the Standard Model is based. Detailed tree-level calculations of physical processes in QED are presented, followed by an elementary treatment of one-loop renormalization of a model scalar field theory, and then by the realistic case of QED. The text includes updates on nucleon structure functions and the status of QED, in particular the precision tests provided by the anomalous magnetic moments of the electron and muon. The authors discuss the main conceptual points of the theory, detail many practical calculations of physical quantities from first principles, and compare these quantitative predictions with experimental results, helping readers improve both their calculation skills and physical insight. Each volume should serve as a valuable handbook for students and researchers in advanced particle physics looking for an introduction to the Standard Model of particle physics. Ian J.R. Aitchison is Emeritus Professor of Physics at the University of Oxford. He has previously held research positions at Brookhaven National Laboratory, Saclay, and the University of Cambridge. He was a visiting professor at the University of Rochester and the University of Washington, and a scientific associate at CERN and SLAC. Dr. Aitchison has published over 90 scientific papers mainly on hadronic physics and quantum field theory. He is the author of two books and joint editor of further two. Anthony J.G. Hey is now Honorary Senior Data Scientist at the UK’s National Laboratory at Harwell. He began his career with a doctorate in particle physics from the University of Oxford. After a career in particle physics that included a professorship at the University of Southampton and research positions at Caltech, MIT and CERN, he moved to Computer Science and founded a parallel computing research group. The group were one of the pioneers of distributed memory message-passing computers and helped establish the ‘MPI’ message passing standard. After leaving Southampton in 2001 he was director of the UK’s ‘eScience’ initiative before becoming a Vice-President in Microsoft Research. He returned to the UK in 2015 as Chief Data Scientist at the U.K.’s Rutherford Appleton Laboratory. He then founded a new ‘Scientific Machine Learning’ group to apply AI technologies to the ‘Big Scientific Data’ generated by the Diamond Synchrotron, the ISIS neutron source, and the Central Laser Facility that are located on the Harwell campus. He is the author of over 100 scientific papers on physics and computing and editor of ‘The Feynman Lectures on Computation’.

Includes bibliographical references

In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schroedinger and Heisenberg frameworks from this perspective and discuss how the momentum map associated to the action of the unitary group on the Hilbert space allows to relate both approaches. We also study Weyl-Wigner approach to Quantum Mechanics and discuss the implications of bi-Hamiltonian structures at the quantum level.

Source: Digital Library of India Scanning Centre: C-DAC, Noida Source Library: Central Library, Bits- Pilani Date Accessioned: 9/23/2015 16:21 The Digital Library of India was a project under the auspices of the Government of India.