A Power-Liouville Hermite Orbit: Common Spectral Quantization of the Singular Sextic Oscillator and Fractional-Power Potentials
The paper establishes an exact four-member power-Liouville Hermite orbit connecting a singular sextic oscillator and two fractional-power potentials. This orbit shows how these different systems share a common physical zero set under specific coordinate transformations, linking energy quantization, coupling quantization, and power duality. It provides an exact discrete sequence for the sextic oscillator's eigencouplings.