Potential Well Bound States-5-4-3-2-1012345-20 -15 -10 -5 0
E (hbar**2/2ma**2)f(E)sqrt
tan
"-cot"Try this 1D Potential Applet. It allows you to vary the potential andsee the eigenstates.
9.1.5 The Potential Barrier
With an analysis of the Potential Barrier problem, we can understand the phenomenon ofquantum
tunneling.
V(x) =
0 x <−a
+V 0 −a < x < a
0 x > aNumbering the three regions from left to right,
u 1 (x) =eikx+Re−ikx
u 2 (x) =Aeκx+Be−κx
u 3 (x) =TeikxAgain we assume a beam of definite momentum incident from the left and no wave incident from
the right. For the solutions outside the barrier,
k=√
2 mE
̄h^2