Thermodynamics, Statistical Physics, and Quantum Mechanics

344 APPENDIXES

Appendix 7:

Variational Calculations

The general procedure forsolvingvariationalproblems in one dimension

is to first evaluate three integrals which are functions ofthe variational

parameter

The two expressions for the kineticenergy K can be shown to beequal

by an integrationby parts. Thesecondexpression is usuallyeasier to use,

since one has to take a singlederivative of thetrial function and then

square it.

Appendix 8:

Normalized Eigenstates of Hydrogen Atom