This second edition of Some Unusual Topics in Quantum Mechanics builds upon the topics covered in the first, with additional chapters that delve deeper into the mathematical foundations of the subject. New topics include Hilbert spaces and unbounded operators, minimum uncertainty states, path integrals in general coordinates, Fock spaces, second quantization, relativistic particle states, and quantum fields. Historical insights are also included, such as a pre-history of matrix mechanics and Pauli's proof of the H-atom spectrum using O(4) symmetry. Finally, readers are introduced to Bell's inequality and the non-locality in quantum mechanics that is revealed through its violation. These topics are rarely covered in introductory textbooks but are crucial to developing a student's interest and deeper understanding of quantum mechanics. This book serves as valuable supporting material for graduate-level core courses on the subject.
1st edition: Position operators of non-relativistic quantum
mechanics.- A bundle picture of quantum mechanics.- A beam of particles = a
plane wave?.- Star-product formulation of quantum mechanics.- Can there be a
non-linear quantum mechanics?.- Interaction = exchange of quanta.- Proof of
Wigner's theorem. 2nd edition new topics: A very brief history of Matrix
mechanics.- Hydrogen atom and O(4).- Minimum Uncertainty States.- Time Energy
Uncertainty Relations?.- Force = curvature in Quantum Mechanics too!.- What
is an essentially self-adjoint operator?.- Time re-parametrization in
path-integrals.- What are rigged Hilbert spaces?.- Relativistic configuration
states, Dirac and Weyl equations.
Pankaj Sharan is a professor retired from the Department of Physics at Jamia Millia Islamia, New Delhi. His research interests are chiefly in quantum mechanics, quantum field theory and general relativity. Over a teaching career spanning four decades, he has taught courses on quantum mechanics, quantum field theory, classical mechanics, general relativity and mathematical physics. He is the author of the book Spacetime, Geometry and Gravitation (Birkhäuser, 2009).
