Question

For a ﬁnite square well of depth −V0 for −a < x < a where
V0 > 0, consider the ground state of the bound state problem
with energy −V0 < E < 0. In regions I (x < −a), II (−a
< x < a), and III (a < x), we can write

ψI = Ae^−κx + Be^κx

ψII = Dcos(lx)

ψIII = Ee^κx + Fe^−κx

(a) What are κ and l in terms (as needed) of E, V0, m,
hbar?

(b) The wave function must be square integrable. What, if any, of
the constants A, B,E, F must equal 0?

(c) What are the boundary conditions on the wave function and its
derivative at x = −a and x = a? (Write down the four equations: two
equations for x = −a and two equations for x = a.)

Answer #1

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