The concept of time dependent Schrödinger equation (TDSE) illustrated in literature and even during class room teaching is mostly either complex or meant for advanced learners. This article is intended to enlighten the concept to the beginners in the field and further to improve knowledge about detailed steps for abstract mathematical formulation used which helps in understanding to derive TDSE using various tools and in more comprehensible manner. It is shown that TDSE may be derived using wave mechanics, time independent equation, classical & Hamilton-Jacobi’s equations. Similar attempts have been done earlier by some researchers. However, this article provides a comprehensive, lucid and well derived derivation, derived using various approaches, which would make this article unique.The concept of time dependent Schrödinger equation (TDSE) illustrated in literature and even during class room teaching is mostly either complex or meant for advanced learners. This article is intended to enlighten the concept to the beginners in the field and further to improve knowledge about detailed steps for abstract mathematical formulation used which helps in understanding to derive TDSE using various tools and in more comprehensible manner. It is shown that TDSE may be derived using wave mechanics, time independent equation, classical & Hamilton-Jacobi’s equations. Similar attempts have been done earlier by some researchers. However, this article provides a comprehensive, lucid and well derived derivation, derived using various approaches, which would make this article unique.

May 1, 20155 citations

On the time-dependent solutions of the Schrödinger equation

Alejandro Palma, I. Pedraza

Progress in theoretical chemistry and physicsJan 1, 20073 citations

Solutions of the Schrödinger equation given by solutions of the Hamilton--Jacobi equation

G. F. Torres del Castillo, C. Sosa Sánchez

We find the form of the potential depending on the coordinates and the time such that a solution, $S$ , of the Hamilton--Jacobi equation yields an exact solution, $\exp ({\rm i} S/\hbar)$ , of the corresponding Schrödinger equation.We find the form of the potential depending on the coordinates and the time such that a solution, $S$, of the Hamilton--Jacobi equation yields an exact solution, $\exp ({\rm i} S/\hbar)$, of the corresponding Schrödinger equation.

arXiv:1605.04277Revista Mexicana de FísicaJan 1, 20164 citations

We find the form of the potential depending on the coordinates and the time such that a solution,

S

, of the Hamilton--Jacobi equation yields an exact solution,

\exp ({\rm i} S/\hbar)

, of the corresponding Schrödinger equation.