Thermodynamics, Statistical Physics, and Quantum Mechanics

The optimal value of called is obtained by finding the minimum value

of

Note that this result is also the first asymmetric state of the potential in
Problem 5.32.

5.34 Return of Combined Potential (Tennessee)

a) The potential contains a term which diverges as as
The only way integrals such as are well defined at the origin
is if this divergence is canceled by factors in In particular, we must have
at small This shows that the wave function must vanish at
This means that a particle on the right of the origin stays there.

b) The bound state must be in the region since only here is the
potential attractive. The trial wave function is

where the variational parameter is We evaluate the three integrals in
(A.3.1)–(A.3.4), where the variable

QUANTUM MECHANICS 281