Assignment:
A particle of mass m moves in the potential
V(x) = -g*delta(x) x>-a
infinity x<-a
(delta (x) = dirac delta function)
a. Without worrying about continuity or boundary conditions, write down the general solution of the Schrodinger equation for a bound state (energy E<0) in regions( -a less than x less than 0) and x>0.
b. In terms of your solution in part (a), write down the boundary conditions at
x=-a and continuity conditions at x=0.
c. From the conditions in part (b), derive a transcendental equation determining the bound state energy E. Solve the equation in the limit as a approaches infinity.