Physics 452 Quantum mechanics II Winter 2012 Karine Chesnel

Homework Phys 452 Next week NO CLASS on Monday Jan 16 Tuesday Jan 17: 6.1,6.2,6.3,6.4 Thursday Jan 19: 6.6, 6.8, 6.9, 6.10

Perturbation theory Phys 452 Ideal theoretical potential Actual realistic potential 0 a Ideal gas Electron- electron Interactions in atoms 0 a Illustration of perturbation

Perturbation theory Phys 452 Unperturbed Hamiltonian Perturbation What is the height of the trees at the top of Half-Dome?

Perturbation theory Phys 452 Unperturbed states Building the wave functions and energy levels to some order zero- order first- order second- order

Quiz 4a What is the diameter of the planetarium dome on the top of the Eyring science building? A. 1 m B. 10 m C. 20 m D. 50 m E. 100 m

Perturbation theory First-order correction Phys 452 Energy State Only works if the energies are non-degenerate

Phys 452 Quiz 4b What is the first order correction to the energies if the perturbation is proportional to the unperturbed Hamiltonian? A. B. C. D. E.

Perturbation theory Second-order correction Phys 452 Energy Only works if the energies are non-degenerate

Perturbation theory Examples Phys a a/2 Ideal gas lattice Delta function inside infinite square well Unperturbed states Pb 6.1 Pb 6.4

Perturbation theory Examples Phys 452 Spring constant expansion in the harmonic oscillator Unperturbed states Here x V Pb 6.2

Perturbation theory Examples Phys a Two particles interacting Find the ground and excited states for the 2-particles systems Pb 6.3