In Section 2.6 we noted that the finite square well (in one dimension) has at least one bound state, no matter how shallow or narrow it may be. In Problem 4.11 you showed that the finite spherical well (three dimensions) has no bound state, if the potential is sufficiently weak. Question: What about the finite circular well (two dimensions)? Show that (like the one-dimensional case) there is always at least one bound state.

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Problem 4.11 A particle of mass m is placed in a finite spherical well: -lo. V(r) = -Vo. r ≤a; r> a. Find the ground state, by solving the radial equation with = 0). Show that there is no bound state if Voa² <² <л²h²/8m.