Spherical Harmonic Oscillators

Published 30 Mar 2025 in math-ph and math.MP | (2503.23549v1)

Abstract: A linear quantum harmonic oscillator factors into one dimensional oscillators and can be solved using creation and annihilation operators. We consider a spherical analogue (there is an obvious hyperbolic analogue, and natural geometric generalizations). This analogue does not factor, and in fact the two dimensional case is critical and has potential applications to chiral models in 2d quantum field theory.

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