# Mathematical Foundations of Quantum Mechanics

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*K. P. Parthasarathy*

A publication of Hindustan Book Agency

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.