 #1
Eitan Levy
 259
 11
 Homework Statement:

A particle with mass m is in a one dimensional potential, as seen below.
The wave function in [itex]x<0[/itex] is 0.
The wave function in [itex]0<x<b[/itex] is: [itex]Asin(kx)[/itex]
The wave function in [itex]x>b[/itex] is: [itex]Be^{\alpha x}[/itex]
It is known that [itex]k=3*10^{10}[/itex] and [itex]b=0.5333333*10^{10}[/itex]
Find [itex]\alpha[/itex]
 Relevant Equations:
 Schrodinger stationary equation
What I tried to do was using the fact that the wave function should be continuous.
[itex]Asin(kb)=Be^{\alpha b}[/itex]
The derivative also should be continuous:
[itex]kAcos(kb)=\alpha Be^{\alpha b}[/itex]
And the probability to find the particle in total should be 1:
[itex]\int_0^b A^2sin^2(kx) dx + \int_b^{\infty} B^2e^{2\alpha x} dx =1 [/itex]
This set of equations is to hard to deal with, the equations should be solved with calculator only so I think I did something wrong.
Also, there may be a better way to approach this problem, but I'm not seeing it.