Quasi-exact solution of sextic anharmonic oscillator using a quotient polynomial

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.


quasi-exactly solvable potentials; sextic anharmonic oscillator; quotient polynomial; energy-reflection symmetry

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