Quantum Chemistry I › Unit 2 · The variational game

The Variational Principle by Hand

Pick a parameterized trial wavefunction, write the energy as a function of the parameters, and minimize — the upper-bound calculation at the root of every electronic-structure method. 8 problems, one per page — start with the worked example, then work down.

1. 1 worked Helium in one parameter — every integral shown →
2. 2 practice When the trial contains the exact answer →
3. 3 practice A basis of the wrong shape →
4. 4 practice A parameter-free trial on a different system →
5. 5 practice Reading a physical constant out of the optimum →
6. 6 practice Linear variation — the secular equation →
7. 7 check An energy below exact →
8. 8 check Why the bound is for the ground state only →

← The whole course problem set