Square potential well with a sinusoidal deep

A square potential well with a sinusoidal deep refers to a quantum mechanics scenario where a particle is confined within a potential well that has a square shape overall but contains a sinusoidal oscillation in its depth. This type of potential well is a variation of the standard square well and can be used to study interesting quantum phenomena.

This potential well can lead to interesting quantum mechanical effects due to the combined influence of the square potential and the sinusoidal modulation. The solutions to the Schrödinger equation within this potential well can be analysed to understand the behaviour of particles in such a system.

Analysing the solutions to this equation can provide insights into the quantized energy levels and corresponding wave functions for particles confined within the square potential well with a sinusoidal deep. The sinusoidal modulation introduces additional features and complexities compared to a standard square well, making it a fascinating system for studying quantum mechanics.

The potential energy function for a particle in a one-dimensional square potential well with a sinusoidal deep can be written as:

First order correction to energy

Only odd value of n contribute non zero value

Second order correction to energy

This note is a part of the Physics Repository.