Wave function in infinite square well, with potential step

[slasakai]

Homework Statement

A Particle energy A trapped in infinite square well. U(x)=0 for 0<x<L and U(x)=U0 for L<x<2L. find the wave function of the particle when A) E>U0 B) E<U0 C) E=U0.

Homework Equations

1-D time independent Schrödinger equation.

The Attempt at a Solution

I have the correct wavefunctions for the particle from 0<x<L and L<x<2L ,(have checked solutions) however I don't understand how to write join them together into one function.

any help would be appreciated, I am new to this subject so please go easy on me haha.

thanks in advance,

S.

 

[BvU]

When you say "I have the correct wavefunctions" you mean general solutions with integration constants ? Those can be found by applying the proper boundary conditions: that way you "join" the wavefunctions . So under 2. you should list some of these conditions.