hw44 - PHYS 455 Homework IV Assigned: November 29, 2011,...

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: PHYS 455 Homework IV Assigned: November 29, 2011, Tuesday. Due: December 7, 2011, Wednesday. 1. Consider an ensemble for a spin-1/2 particle where the particle is in “spin-up along z ” state with probability p 1 = 1 / 6, “spin-down along z ” state with probability p 2 = 1 / 3, and “spin-up along x ” state with probability p 3 = 1 / 2. (a) Compute the density matrix ρ of this ensemble. (b) As an example, compute the expectation value of σ z , by using (i) the density matrix and (ii) the ensemble states and probabilities. 2. Consider a mixed state with the following matrix ρ = 1 5 • 2 1 + i 1- i 3 ‚ . (a) Is this really a valid density matrix? (In other words, does ρ satisfy all of the condi- tions that a density matrix should satisfy?) (b) Compute h σ x i , h σ y i and h σ z i . Express your results compactly by expressing h ~σ i . (b ) The vector h ~σ i expresses the position of the mixed state ρ inside the Bloch sphere....
View Full Document

This note was uploaded on 02/11/2012 for the course MATH 435 taught by Professor Starg during the Spring '11 term at Al Ahliyya Amman University.

Page1 / 2

hw44 - PHYS 455 Homework IV Assigned: November 29, 2011,...

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