Find the solution to the TISE for the case 
. Be
certain that your solution satisfies all appropriate conditions.
You need not normalize your wave function. In your solution, let
be the de Broglie wave vector for the particles when x;SPMlt;0 and
be the de Broglie wave vector for the particles when x;SPMgt;0.
Hint: Choosing
solutions of the form 
, 
, 
,
will simplify your algebra considerably.
Make two sketches of your wave function for cases where 
so that 
. The first sketch should be in a case where
, and the second for a case where 
, where n is an integer.
Pay particular attention to the relative amplitude of the oscillations
of the wave functions for x;SPMlt;0 as compared to x;SPMgt;0.