- #1

gfd43tg

Gold Member

- 950

- 50

## Homework Statement

## Homework Equations

## The Attempt at a Solution

a) The schrödinger equation

$$i \hbar \frac {\partial \Psi}{\partial t} = - \frac {\hbar^{2}}{2m} \nabla^{2} \psi + V \psi $$

For the case ##0 \le x,y,z \le a##, ##V = 0##

$$i \hbar \frac {\partial \Psi}{\partial t} = - \frac {\hbar^{2}}{2m} \Big [ \frac {\partial^{2} \psi}{\partial x^{2}} + \frac {\partial^{2} \psi}{\partial y^{2}}+ \frac {\partial^{2} \psi}{\partial z^{2}} \Big ]$$

But with the sum of the second derivates, is it possible to set each of these equal to the time derivative separately? If so, then why?