function potential: as Seen in Solver Scenario 5
Figure 3: Dirac potential, strength D
As we discussed in class, in all cases where the potential is
finite, the derivatives of the wave functions for the pure energy
states, 
, remain continuous across all boundaries.
If the potential V(x) contains a function at the point
x=a of strength D, 
, then the potential is no
longer finite at the point x=a, and there is a discontinuity in the
slope. The function, however is not strong enough to
generate a discontinuity in the wave function itself.
As we will show in lecture on Thursday, this discontinuity has magnitude
where 
is the solution to the right of the
function (x;SPMgt;a) and 
is the solution to the left of
the function (x;SPMlt;a). We use 
in the expression (2)
because it does not matter which part of the solution one uses for (
wave function is continuous at a: 
).
