Mathematical Physics


Quasi-Exactly Solving the Sextic Anharmonic Oscillator Using a Quotient Polynomial

Authors: Spiros Konstantogiannis

Among the one-dimensional, smooth and real polynomial potentials, the sextic anharmonic oscillator is the only one that can be quasi-exactly solved [6, 7], in the sense that it is expressed in terms of a non-negative integer n and for every value of n, we can find n+1 energies and the respective eigenfunctions in closed form. In this work, we use, as basic parameter, the constant term of a quotient polynomial [3], to quasi-exactly solve the sextic anharmonic oscillator and demonstrate that the new parameter is a preferential one to study the system, as it makes the analysis straightforward and transparent.

Comments: 33 Pages.

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Submission history

[v1] 2017-09-03 04:28:49
[v2] 2017-09-05 06:02:43

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