Quantum Square Well Bound States Described by Equations with Non-locality

TL;DR

This paper introduces a novel equation that explicitly incorporates non-locality to accurately describe quantized energy levels in quantum square well bound states, inspired by delayed feedback in differential equations.

Contribution

It presents a new non-local equation for quantum bound states, bridging quantum mechanics with non-local differential equations influenced by delayed feedback studies.

Findings

Successfully reproduces quantized energy levels

Provides a new perspective on non-local quantum equations

Connects quantum bound states with delayed feedback models

Abstract

We present here a simple equation explicitly incorporating non-locality, which reproduces quantized energy levels of the bound states for the square well potentials. Introduction of this equation is motivated by studies of differential equation with time delayed feedback, which can be viewed as describing temporal non-locality.