Question

Estimate of the second shallowest bound state?

Answer 1

Suppose we have a 1D potential V(x) of finite range, i.e.,

V(x) = 0

for |x|>b. The potential is assume to support at least two bound states, but might have more, say n≥2.

The shallowest one En<0 can be infinitesimally small. However, how about the second shallowest one En−1<En

Answer 2

I emphasize that the shallowest bound state En is the highest excited bound state. Do not confuse it with the ground state E1! It is apparent that this state En can be arbitrarily close the continuum edge.