Quantum Hamilton-Jacobi Formalism

Beschreibung

This book describes the Hamilton-Jacobi formalism of quantum mechanics, which allowscomputation of eigenvalues of quantum mechanical potential problems without solving for thewave 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. Advancedundergraduates having knowledge of complex variables and quantum mechanics will find thisas an interesting method to obtain the eigenvalues and eigen-functions. The discussion oncomplex zeros of the wave function gives intriguing new results which are relevant foradvanced students and young researchers. Moreover, a few open problems in research arediscussed as well, which pose a challenge to the mathematically oriented readers.
A well-trained undergraduate student will learn a new and elegant method of solving quantum mechanical problems An experienced reader can follow the treatment of several diverse and exotic models within a single formalism The book examines some interesting challenges which will be of interest to a serious researcher

Autor*in

A. K. Kapoor

Themen in »Quantum Hamilton-Jacobi Formalism«

quantum Hamilton-Jacobi formalism exact quantization condition rational extension of potential models exceptional orthogonal polynomials complex Scarf-II potential and optical systems PT symmetry classification of exactly and quasi exactly solvable models

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“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)
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