Mathematical foundations of quantum mechanics [electronic resource] / K. R. Parthasarathy.

Call Number	530.12
Author	Parthasarathy, K. R.
Title	Mathematical foundations of quantum mechanics K. R. Parthasarathy.
Edition	1st ed.
Physical Description	1 online resource (184 pages)
Series	Texts and Readings in Mathematics ; 35
Contents	Mathematical foundations of quantum mechanics -- Contents -- Preface -- Chapter 1: Probability Theory on the Lattice of Projections in a Hilbert Space -- Chapter 2: Systems with a Configuration Under a Group Action -- Chapter 3: Multipliers on Locally Compact Groups -- Chapter 4: The Basic Observables of a Quantum Mechanical System -- Bibliography -- Index -- Texts and Readings in Mathematics.
Summary	This is a brief introduction to the mathematical foundations of quantum mechanics based on lectures given by the author to Ph.D.students at the Delhi Centre of the Indian Statistical Institute in order to initiate active research in the emerging field of quantum probability. In addition to quantum probability, an understanding of the role of group representations in the development of quantum mechanics is always a fascinating theme for mathematicians. The first chapter deals with the definitions of states, observables and automorphisms of a quantum system through Gleason's theorem, Hahn-Hellinger theorem, and Wigner's theorem. Mackey's imprimitivity theorem and the theorem of inducing representations of groups in stages are proved directly for projective unitary antiunitary representations in the second chapter. Based on a discussion of multipliers on locally compact groups in the third chapter all the well-known observables of classical quantum theory like linear momenta, orbital and spin angular momenta, kinetic and potential energies, gauge operators etc., are derived solely from Galilean covariance in the last chapter. A very short account of observables concerning a relativistic free particle is included.
Subject	MATHEMATICS / General. SCIENCE / Physics / General. Electronic books.
Multimedia	https://portal.igpublish.com/iglibrary/search/HBAB0000014.html

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$a Mathematical foundations of quantum mechanics -- Contents -- Preface -- Chapter 1: Probability Theory on the Lattice of Projections in a Hilbert Space -- Chapter 2: Systems with a Configuration Under a Group Action -- Chapter 3: Multipliers on Locally Compact Groups -- Chapter 4: The Basic Observables of a Quantum Mechanical System -- Bibliography -- Index -- Texts and Readings in Mathematics.

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$a This is a brief introduction to the mathematical foundations of quantum mechanics based on lectures given by the author to Ph.D.students at the Delhi Centre of the Indian Statistical Institute in order to initiate active research in the emerging field of quantum probability. In addition to quantum probability, an understanding of the role of group representations in the development of quantum mechanics is always a fascinating theme for mathematicians. The first chapter deals with the definitions of states, observables and automorphisms of a quantum system through Gleason's theorem, Hahn-Hellinger theorem, and Wigner's theorem. Mackey's imprimitivity theorem and the theorem of inducing representations of groups in stages are proved directly for projective unitary antiunitary representations in the second chapter. Based on a discussion of multipliers on locally compact groups in the third chapter all the well-known observables of classical quantum theory like linear momenta, orbital and spin angular momenta, kinetic and potential energies, gauge operators etc., are derived solely from Galilean covariance in the last chapter. A very short account of observables concerning a relativistic free particle is included.

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Summary	This is a brief introduction to the mathematical foundations of quantum mechanics based on lectures given by the author to Ph.D.students at the Delhi Centre of the Indian Statistical Institute in order to initiate active research in the emerging field of quantum probability. In addition to quantum probability, an understanding of the role of group representations in the development of quantum mechanics is always a fascinating theme for mathematicians. The first chapter deals with the definitions of states, observables and automorphisms of a quantum system through Gleason's theorem, Hahn-Hellinger theorem, and Wigner's theorem. Mackey's imprimitivity theorem and the theorem of inducing representations of groups in stages are proved directly for projective unitary antiunitary representations in the second chapter. Based on a discussion of multipliers on locally compact groups in the third chapter all the well-known observables of classical quantum theory like linear momenta, orbital and spin angular momenta, kinetic and potential energies, gauge operators etc., are derived solely from Galilean covariance in the last chapter. A very short account of observables concerning a relativistic free particle is included.
Contents	Mathematical foundations of quantum mechanics -- Contents -- Preface -- Chapter 1: Probability Theory on the Lattice of Projections in a Hilbert Space -- Chapter 2: Systems with a Configuration Under a Group Action -- Chapter 3: Multipliers on Locally Compact Groups -- Chapter 4: The Basic Observables of a Quantum Mechanical System -- Bibliography -- Index -- Texts and Readings in Mathematics.
Subject	MATHEMATICS / General. SCIENCE / Physics / General. Electronic books.
Multimedia	https://portal.igpublish.com/iglibrary/search/HBAB0000014.html