A Laplace transform approach to the quantum harmonic oscillator

TL;DR

This paper applies the Laplace transform method to analyze the one-dimensional quantum harmonic oscillator, deriving its stationary states by enforcing parity and boundary conditions.

Contribution

It introduces a Laplace transform approach to solve the quantum harmonic oscillator, providing an alternative method to traditional differential equation techniques.

Findings

Stationary states are obtained using Laplace transforms.

Parity and boundary conditions are crucial for solutions.

The method offers a new perspective on solving quantum oscillators.

Abstract

The one-dimensional quantum harmonic oscillator problem is examined via the Laplace transform method. The stationary states are determined by requiring definite parity and good behaviour of the eigenfunction at the origin and at infinity.