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Quantum Hamilton - Jacobi soluton for spectra of several one dimensional potentials with special properties

S. Sree Ranjani
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Abstract

In this thesis the quantum Hamilton - Jacobi (QHJ) formalism is used for (i) potentials which exhibit different spectra for different ranges of the potential parameters, (ii) exactly solvable (ES) periodic potentials (iii) quasi - exactly solvable (QES) periodic potentials and (iv) the PT symmetric potentials (ES and QES). The QHJ formalism provides a simple and elegant method to obtain the bound state and the band edge eigenvalues and the eigenfunctions. For this purpose, a simple conjecture on the singularities of the logarithmic derivative of the wave function in the complex plane is made and used in a straight forward fashion to obtain the desired results.

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S. Sree Ranjani. 2004-08-05. Quantum Hamilton - Jacobi soluton for spectra of several one dimensional potentials with special properties. https://arxiv.org/abs/quant-ph/0408036

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