Generalized Solutions for Quantum Mechanical Oscillator on K\"{a}hler Conifold

TL;DR

This paper explores generalized boundary conditions for a quantum oscillator on Kähler conifold, revealing how these conditions affect spectral degeneracies and recovering known spectra through self-adjoint extensions.

Contribution

It introduces a framework for boundary conditions via self-adjoint extensions, showing their impact on spectral degeneracies in quantum oscillators on Kähler conifolds.

Findings

Generalized boundary conditions can restore orbital angular momentum degeneracy.

The known spectrum is recovered under specific boundary conditions.

Self-adjoint extension method effectively characterizes boundary effects.

Abstract

We study the possible generalized boundary conditions and the corresponding solutions for the quantum mechanical oscillator model on K\"{a}hler conifold. We perform it by self-adjoint extension of the the initial domain of the effective radial Hamiltonian. Remarkable effect of this generalized boundary condition is that at certain boundary condition the orbital angular momentum degeneracy is restored! We also recover the known spectrum in our formulation, which of course correspond to some other boundary condition.