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Mathematical Foundations of Quantum Mechanics
K. P. Parthasarathy, Indian Statistical Institute, New Delhi, India
A publication of Hindustan Book Agency.
Hindustan Book Agency
2005; 184 pp; hardcover
ISBN-10: 81-85931-59-3
ISBN-13: 978-81-85931-59-3
List Price: US$34
Member Price: US$27.20
Order Code: HIN/26
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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.

In conclusion, the spectral theory of Schrodinger operators of one and two electron atoms is discussed in some detail.

A publication of Hindustan Book Agency; distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels.

Readership

Graduate students and research mathematicians interested in mathematical physics.

Table of Contents

  • Probability theory on the lattice of projections in a Hilbert space
  • Systems with a configuration under a group action
  • Multipliers on locally compact groups
  • The basic observables of a quantum mechanical system
  • Bibliography
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