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arXiv:0805.3152 · Journal of Physics A Mathematical and Theoretical

New approach to separable bounded quantum-mechanical models

Francisco Marcelo Fernández

Published Jul 22, 2008• 1 citation
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Abstract

We develop an approach for the treatment of one--dimensional bounded quantum--mechanical models by straightforward modification of a successful method for unbounded ones. We apply the new approach to a simple example and show that it provides solutions to both the bounded and unbounded type of models simultaneously
DOI
10.1088/1751-8113/41/33/335210

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We propose a simple and straightforward method based on Wronskians for the calculation of bound-state energies and wavefunctions of one-dimensional quantum-mechanical problems. We explicitly discuss the asymptotic behaviour of the wavefunction and show that the allowed energies make the divergent part vanish. As illustrative examples we consider an exactly solvable model, the Gaussian potential well, and a two-well potential proposed earlier for the interpretation of the infrared spectrum of ammonia.