Thermodynamics, Statistical Physics, and Quantum Mechanics

65

a) Using the normalized trialfunction

find the value of which minimizes the ground stateenergy and

the resulting estimate of the ground state energy. How is this value

related to the true ground state energy?

What is the exact ground state wave function and energy for this

system (neglect the normalization of the wave function)? Do not

solve the Schrödinger equation directly. Rather, state the answer and

justify it.

Hint:You may need theintegral

b)

5.37 Helium Atom (Tennessee)

Do a variational calculation to estimate the ground state energy of the
electrons in the helium atom. The Hamiltonian for two electrons, assuming
the nucleus is fixed, is

QUANTUM MECHANICS