852_2010hw4 - PHYS852 Quantum Mechanics II, Spring 2010...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight 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 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

Page1 / 2

852_2010hw4 - PHYS852 Quantum Mechanics II, Spring 2010...

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