Mathematical Physics


Quasi-Exact Solution of Sextic Anharmonic Oscillator Using a Quotient Polynomial

Authors: Spiros Konstantogiannis

Among the one-dimensional, real and analytic polynomial potentials, the sextic anharmonic oscillator is the only one that can be quasi-exactly solved, if it is properly parametrized. In this work, we present a new method to quasi-exactly solve the sextic anharmonic oscillator and apply it to derive specific solutions. Our approach is based on the introduction of a quotient polynomial and can also be used to study the solvability of symmetrized (non-analytic) or complex PT-symmetric polynomial potentials, where it opens up new options.

Comments: 18 Pages. Published on the Journal for Foundations and Applications of Physics, vol. 6, No. 1 (2019), pp. 17-34

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Submission history

[v1] 2017-09-03 04:28:49
[v2] 2017-09-05 06:02:43
[v3] 2018-12-16 04:22:28

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