- #1
broegger
- 257
- 0
I'm trying to normalize the even wave functions for the finite square well. The wave function is:
[tex]
\psi(x)=
\begin{cases}
Fe^{\kappa x} & \text{for } x< a\\
D\cos(lx) & \text{for } -a\leq x \leq a\\
Fe^{-\kappa x} & \text{for } x> a
\end{cases}
[/tex]
How can I determine D and F? When I set
I obtain an equation in the two unknown amplitudes D and F. I could apply some boundary conditions to get more equations, but it gets rather complicated and I know there is an easier way...
[tex]
\psi(x)=
\begin{cases}
Fe^{\kappa x} & \text{for } x< a\\
D\cos(lx) & \text{for } -a\leq x \leq a\\
Fe^{-\kappa x} & \text{for } x> a
\end{cases}
[/tex]
How can I determine D and F? When I set
[tex]\int_{-\infty}^{\infty}|\psi(x)|^2dx = 1[/tex],
I obtain an equation in the two unknown amplitudes D and F. I could apply some boundary conditions to get more equations, but it gets rather complicated and I know there is an easier way...