set7 - Department of Physics The Ohio State University...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Department of Physics Prof. R. Bundschuh The Ohio State University Seventh Problem Set for Physics 847 (Statistical Physics II) Winter quarter 2004 Important date: Mar 16 9:30am-11:18am Fnal exam Due date: Tuesday, ±eb 24 18. Spin 1 atom 12 points An atom with spin 1 has a Hamiltonian ˆ H = A ˆ S 2 z + B ( ˆ S 2 x - ˆ S 2 y ), where ˆ S x , ˆ S y , and ˆ S z are the x , y , and z component of the spin angular momentum operator. In the basis of eigenstates of the operator ˆ S z these three operators have the matrix representations ˆ S z = ¯ h 1 0 0 0 0 0 0 0 - 1 , ˆ S x = ¯ h 2 0 1 0 1 0 1 0 1 0 , and ˆ S y = ¯ h i 2 0 1 0 - 1 0 1 0 - 1 0 . At time t = 0 the atom is initially in an eigenstate of ˆ S z with eigenvalue +¯ h . a) Write the density matrix (in the basis of eigenstates of ˆ S z ) at t = 0. b) Compute the density matrix at time t in the basis of eigenstates of ˆ S z .
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 07/17/2008 for the course PHYS 847 taught by Professor Bundschuh during the Winter '04 term at Ohio State.

Page1 / 2

set7 - Department of Physics The Ohio State University...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online