- #1

Matthew888

- 8

- 0

## Homework Statement

Consider a particle (which mass is [tex]m[/tex]) and the following unidimensional potential:

[tex]V(x)=\begin{cases}+\infty & x<0\\ -V_0 & 0<x<a\\0 & x>a \end{cases}[/tex]

Let [tex]E[/tex] be positive. Find the spatial autofunction.

## Homework Equations

I'm convinced that I have to use Schroedinger's equation.

## The Attempt at a Solution

I found:

[tex]\psi(x)=\begin{cases} 0 & x<0 \\ A\sin{lx}+B\cos{lx} & 0<x<a\\ C\exp{ikx}+D\exp{-ikx} & x>a\end{cases}[/tex]

where [tex]k=\frac{\sqrt(2mE)}{\bar{h}}[/tex] and [tex]l=\frac{\sqrt{2m(E+V_0)}}{\bar{h}}[/tex].

Is this correct?