2 and 3-dimensional Hamiltonians with Shape Invariance Symmetry

TL;DR

This paper derives 2D and 3D Hamiltonians with shape invariance symmetry through dimensional reduction and demonstrates their eigenspectra and equivalence to Lie algebraic symmetry.

Contribution

It introduces a novel dimensional reduction method to obtain Hamiltonians with shape invariance symmetry and establishes their equivalence to Lie algebraic symmetry.

Findings

Derived 2D and 3D Hamiltonians with shape invariance symmetry.

Obtained eigenspectra of these Hamiltonians.

Showed equivalence between shape invariance and Lie algebraic symmetry.

Abstract

Via a special dimensional reduction, that is, Fourier transforming over one of the coordinates of Casimir operator of su(2) Lie algebra and 4-oscillator Hamiltonian, we have obtained 2 and 3 dimensional Hamiltonian with shape invariance symmetry. Using this symmetry we have obtained their eigenspectrum. In the mean time we show equivalence of shape invariance symmetry and Lie algebraic symmetry of these Hamiltonians.