130_notes.dvi

25.4 The Variational Principle (Rayleigh-Ritz Approximation)

Because the ground state has the lowest possible energy, we can vary a test wavefunction, minimizing
the energy, to get a good estimate of the ground state energy.

HψE=EψE

for the ground stateψE.

E=

∫

ψ∗EHψEdx

∫

ψ∗EψEdx

For any trial wavefunctionψ,

E′=

∫

ψ∗Hψdx

∫

ψ∗ψdx

=

〈ψ∗|H|ψ〉

〈ψ|ψ〉