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

2004/08/05 by S. Sree Ranjani, Ranjani, S. Sree
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/0408036

Thesis submitted to the University of Hyderabad (2004)

arxiv created 2004/08/05 · arxiv updated 2009/12/01

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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