- #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.