Schrodinger Equation: Particle in a Box

[jgens]

Homework Statement

We have been examining a one-dimensional infinite square well where the infinite walls are located at -b and +b. The energy levels in this quantum system are non-degenerate, that is for each energy there is only one wave function. Let us place an infinite potential step between -b/2 and +b/2.

• Is the particle more likely to be in the left or the right infinite square well?
• What are the new energy levels and wave functions of this modified system?
• Are the energy levels degenerate, and if so, what is the degeneracy?
• Are the new energies higher or lower than the box without the infinite step?

Homework Equations

Time-independent Schrödinger Equation

The Attempt at a Solution

My main question involves how to interpret this problem. In my reading, the potential is just V(x) = 0 for -b < x < a and V(x) = +infinity for a < x < b where -b/2 < a < b/2. If my reading is correct, then wouldn't the particle only be in the left square well? (Since any particle would just be reflected from the region with infinite potential)

Thanks

 

[Spinnor]

I read it the same way, all the step does is to reduce the width of the well.

 

[vela]

I read it to mean that V(x)=0 for -b≤x≤-b/2 or b/2≤x≤b and V(x)=infinity everywhere else.