This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: PHYS852 Quantum Mechanics II, Spring 2010 HOMEWORK ASSIGNMENT 4 Topics covered: rotation with spin, exchange symmmetry 1. A vector pointing in the , direction, can be formed by starting with a vector pointing along vectore z , then applying an active rotation by about the y-axis, followed by a rotation by about the z-axis. (a) Verify this for an ordinary vector, by starting with the vector (0 , , 1) T and using R y ( ) = cos 0 sin 1 sin 0 cos ; R z ( ) = cos sin sin cos 1 (1) (b) Thus for a spin-1/2 system, the spin-up state with respect to the , direction can be found in the basis of S z eigenstates, by starting with the spin-up state along vector e z , and applying unitary rotation operators, i.e. | ) = e- i planckover2pi1 S z e- i planckover2pi1 S y | z ) . (2) In this way, find the states | ) and | ) ....
View Full Document
- Spring '11