Few quantum mechanical models in higher dimension-framed with Elzaki transform

TL;DR

This paper introduces a novel application of the Elzaki transform to solve the N-dimensional Schrödinger equation in quantum mechanics, providing a universal method for handling complex differential equations in multiple dimensions.

Contribution

It is the first to apply the Elzaki transform in non-relativistic quantum mechanics for multidimensional Schrödinger equations, developing a formula-based approach for non-constant coefficient differential equations.

Findings

Successfully solved N-dimensional Schrödinger equations with Elzaki transform

Developed a universal transformation scheme for quantum differential equations

Provided closed-form solutions for various solvable potentials

Abstract

Very first time Elzaki transform is used in non relativistic quantum mechanics to solve $N$-dimensional Schr\"{o}dinger equation in a closed form for different solvable potential models. A universal transformation scheme is introduced and a formula based approach is developed which shows how to apply Elzaki transform to differential equation with non-constant coefficients that generally appear in solving quantum mechanical initial value problems specially for multidimensional Schr\"{o}dinger equation.