Method for calculating analytical solutions of the Schrödinger equation: Anharmonic oscillators and generalized Morse oscillators
- 1 April 1996
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 53 (4) , 2009-2020
- https://doi.org/10.1103/physreva.53.2009
Abstract
A method for calculating the analytical solutions of the one-dimensional Schrödinger equation is suggested. A general discussion of the possible forms of the potentials and wave functions that are necessary to get the analytical solution is presented. In general, the analytical solutions appear in multiplets corresponding to the quantum number n of the harmonic oscillator. As an application, known solutions for the anharmonic oscillators are critically recalculated and a few additional results are found. Analytical solutions are also found for the generalized Morse oscillators. © 1996 The American Physical Society.Keywords
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