A square root of the harmonic oscillator

TL;DR

This paper introduces a novel oscillator model with a Hamiltonian that admits an exact square root, incorporating the parity operator, offering an alternative to traditional creation and annihilation operator methods.

Contribution

It presents a new oscillator model with an exact square root Hamiltonian using the parity operator, expanding the theoretical framework beyond conventional approaches.

Findings

Constructed an oscillator model with an exact square root Hamiltonian.

Outlined the solution method and potential generalizations.

Provides a theoretical foundation for alternative oscillator models.

Abstract

Allowing for the inclusion of the parity operator, it is possible to construct an oscillator model whose Hamiltonian admits an EXACT square root, which is different from the conventional approach based on creation and annihilation operators. We outline such a model, the method of solution and some generalizations.