852_2010hw5 - PHYS852 Quantum Mechanics II, Spring 2010...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: PHYS852 Quantum Mechanics II, Spring 2010 HOMEWORK ASSIGNMENT 5 Topics covered: rotation with spin, exchange symmmetry 1. The Hamiltonian for the deuteron, a bound-state of a proton and neutron, may be written in the form H = P 2 p 2 M p + P 2 n 2 M n + V 1 ( R ) + V 2 ( R ) ~ S p ~ S n , (1) where R is the relative radial coordinate. Both are spin-1/2 particles, but they are not identical. (a) The total angular momentum operator is ~ S = ~ S p + ~ S n . The state | s p s n sm i is the simultaneous eigenstate of ~ S p , ~ S n , S 2 , and S z . What are the allowed values of the total spin quantum number s ? For each s-value, what are the allowed m quantum numbers. (b) Show that | s p s n sm i is an eigenstate of ~ S p ~ S n , and give the corresponding eigenvalue. Hint, use the fact that S 2 = ( ~ S p + ~ S n ) ( ~ S p + ~ S n ). (c) Give ten distinct quantum numbers that can be assigned to an eigenstates of this H . Note that this includes s p and s n , even though they can never change., even though they can never change....
View Full Document

Ask a homework question - tutors are online