Answer to Question #126925 in Quantum Mechanics for christopher seebaran

Question

 State the time-dependent Schrodinger equation in three dimensions. State the meaning of all the terms in the equation. 

Answer 1

The time-dependent Schrödinger equation reads

$$i \hbar \frac{\partial}{\partial t}\Psi\\ =-\frac{ \hbar^2}{2m}\left(\dfrac{\partial^2 \Psi}{\partial x^2}+\dfrac{\partial^2 \Psi}{\partial y^2}+\dfrac{\partial^2 \Psi}{\partial z^2}\right)+V(x,y,z)\Psi$$

The function Ψ varies with time t as well as with position x, y, z.

V is assumed to be a real function and represents the potential energy of the system.