3 papers
quant-ph2026
Wallis Products from the Four-Dimensional Singular Harmonic Oscillator
Bin Ye, Ruitao Chen, Lei Yin
We present a variational derivation of the Wallis product and its reciprocal from the four-dimensional singular harmonic oscillator. The inverse-square interaction is absorbed into…
quant-ph2026
Emergence of from Equatorial Quantum Localization
Bin Ye, Ruitao Chen, Lei Yin
We present a genuinely non-radial quantum-mechanical route by which emerges from equatorial localization on the sphere. For the highest-weight branch of spherical harmonics, t…
quant-ph2026
Quantum Realization of the Wallis Formula
Bin Ye, Ruitao Chen, Lei Yin
We present a unified quantum-mechanical derivation of the Wallis formula from two solvable radial systems: the circular states of the three-dimensional isotropic harmonic oscillato…