Day 7 In-Class Activity
Single Dirac Potential Well
Now that we have built up the architecture for dealing with different kinds of wells, let’s set up the problem of bound states of a Dirac Potential Well.
Consider a potential that is given by:
- Question: Sketch the potential well (note the negative sign on the
function) and write down the eigenvalue equation for locations away from .- Discussion: We are seeking bound state solutions. What can you say about the sign of any expected eigenenergies? What does that indicate for the sign of
in a definition of ?
- Discussion: We are seeking bound state solutions. What can you say about the sign of any expected eigenenergies? What does that indicate for the sign of
- Question: With that choice of
, what do the general solutions look like at away from ?- Discussion: Can you argue anything about the value of some of the undetermined coefficients?
- Question: What boundary conditions are appropriate here? Can you write them? No need to solve anything yet.
- Discussion: The potential goes to infinity at
, what does that imply about your boundary conditions?
- Discussion: The potential goes to infinity at