This book describes the Hamilton-Jacobi formalism of quantum mechanics, which allows
computation of eigenvalues of quantum mechanical potential problems without solving for the
wave function. The examples presented include exotic potentials such as quasi-exactly solvable models and Lame an dassociated Lame potentials. A careful application of boundary conditions offers an insight into the nature of solutions of several potential models. Advanced
undergraduates having knowledge of complex variables and quantum mechanics will find this
as an interesting method to obtain the eigenvalues and eigen-functions. The discussion on
complex zeros of the wave function gives intriguing new results which are relevant for
advanced students and young researchers. Moreover, a few open problems in research are
discussed as well, which pose a challenge to the mathematically oriented readers.
The Quantum Hamilton Jacobi Formalism. - Exactly Solvable Models.- New Results on Singularities of QMF.- Rational Shape Invariant Extensions and Exceptional Polynomials.- QHJ in the Context of Other Related Work. This is a short work & consisting of 7 chapters, each of which ends with an extensive list of references. & it is interesting and very well written. & The chapters are basically independent of each other with the second being important for all. & On the whole, for a brief book it does a good job of working through the subject matter it covers. (Paul F. Bracken, Mathematical Reviews, September, 2023)
Ashok K. Kapoor served as a faculty member the School of Physics at the University of Hyderabad from 1979 to 2012. In addition to the teaching and research, he served as the Head of Special Centre of Integrated Studies, University of Hyderabad. He has taught undergraduate and postgraduate courses in many otlă
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