Quantum II (PHYS 4410) Lecture 10 Degenerate perturbation theory HWK 3 is due today at 6PM.

Physics Colloquium 4PM today, Duane G1B20 Prof. Z.X. Shen, Stanford University High Temperature Superconductivity – Insights from Einstein’s Electrons

Physics Colloquium 4PM today, Duane G1B20 Prof. Z.X. Shen, Stanford University High Temperature Superconductivity – Insights from Einstein’s Electrons

150 A)Yep. B)Nope. C)Waaiit a minute… let me think… Have you ever seen a situation in quantum mechanics that involved a special case with a 2-d Hilbert Space and degenerate energies? Examples??

150 A) Still |a> and |b> and degenerate B) Still |a> and |b> but non-degenerate C)  |a> +  |b> and degenerate D)  |a> +  |b> but non-degenerate E) Depends on H’ A 2-d Hilbert Space has states |a> and |b> that are eigen states of some H 0 and that have degenerate energies, both equal to E 0. We change the Hamiltonian to H 0 +H’. The new eigen states are:

150 A) Still |+> and |-> and degenerate B) Still |+> and |-> but non-degenerate C)  and degenerate D) but non-degenerate A spin ½ system is represented with eigen states of S z : |+> and |-> Turn on B-field in x-direction. The new eigen states are:

150 A) E 0 B) 2E 0 C)  E 0 +  E 0 D)Impossible to tell without the specific H 0 A 2-d Hilbert Space has states |a> and |b> that have degenerate energies, both equal to E 0. The most general state vector is  |a> +  |b> This general state has energy equal to: