Applications of Laguerre transform to solve Schr\"{o}dinger-type equations and Differential Equations of order four

TL;DR

This paper demonstrates how the finite Laguerre transform can be used to solve higher-order differential equations and the one-dimensional steady-state Schrödinger equation efficiently using elementary linear algebra techniques.

Contribution

It introduces a novel application of the finite Laguerre transform to solve complex differential equations with a straightforward linear algebra approach.

Findings

Successfully applied Laguerre transform to higher-order differential equations.

Efficient solution method for the Schrödinger equation using elementary linear algebra.

Potential for simplifying complex differential equation problems.

Abstract

The finite Laguerre transform is applied to solve Differential Equations Problems of order higher than two and a one-dimensional steady-state Schr\"{o}dinger equation, by using elementary Linear Algebra methods.