How to Adjust Wave Function for a Particle in an Infinite Tube?

[eit32]

If I know how to get a wave function for a 3-dimensional particle in a box problem, what adjustments must I make to solve the same problem for a particle traveling in the +z direction in a tube of infinite length?

Box:
0<x<a
0<y<b
0<z<c

Tube:
0<x<a
0<y<a
0<z<infinity

 

[lzkelley]

Thats the basic idea. The primary effect of that, is that the wave number in the z direction won't have the same bounds.
Most likely the wave will be a real exponential (decaying or growing) -> and clearly it can't be growing unbounded.

Does that help? Try throwing the new boundary conditions into the differential wave equation.

 

[eit32]

well i think i problem I'm running into is that the wave function for the box isin the form of a sine function Asin((n pi x)/a)sin((n pi y)/b). sin((n pi z)/c). But if i just sub in my infinity then that doesn't really make sense, it just goes to sin(0).

 

[lzkelley]

the z portion is no longer a sin; its going to be e^ -kz for some constant k that you have to find from solving the wave equation with separation of variables.