Thermodynamics, Statistical Physics, and Quantum Mechanics

5.33 Linear Potential II (MIT, Tennessee)

The wave function must vanish in either limit that Two

acceptable variational trial functions are

where the prefactor ensures that the trial function vanish at the origin.
In both cases the variational parameter is We give the solution for the
first one, although either is acceptable. It turns out that (S.5.33.2) gives a
higher estimate for the ground state energy, so (S.5.33.1) is better, since the
estimate of the ground-state energy is always higher than the exact value.
The ground state energy is obtained by evaluating the three integrals in
(A.3.1)–(A.3.4):

280 SOLUTIONS