Problem Set 03 - Physics 424 Quantum Mechanics Fall 2015 Reading\/Homework Assignment 3 Due in Class Friday Reading Finish reading Townsend Chapter 2

Problem Set 03 - Physics 424 Quantum Mechanics Fall 2015...

This preview shows page 1 - 2 out of 3 pages.

Physics 424: Quantum Mechanics, Fall 2015 Reading/Homework Assignment 3 Due in Class Friday, 10/2/15 1 Reading Finish reading Townsend Chapter 2. This is a long and fairly difficult chapter, but it covers many important principles. Start reading Townsend Chapter 3. You don’t need this for the prob- lems below, but we should start covering this material in class by the end of the week. Problems to work out and turn in (55 pts total) 1. (10 pts) Townsend problem 2.1 - Show lim N →∞ (1 + z/N ) N = e z . 2. (5 pts) Consider the projection operator ˆ P α = | α ih α | where | α i is any normalized quantum state. This problem should be done with bras, kets, and operators (no spinors or matrices written out), and so it is valid for Hilbert spaces with any dimension D (so far we have used D = 2 in class). (a) Show that ˆ P 2 α = ˆ P α . (b) Use result 2a to show that the only possible eigenvalues of ˆ P α are zero and one. (c) Show that | α i is an eigenvector of ˆ P α with eigenvalue one, and that any state | β i that is orthogonal to | α
Image of page 1
Image of page 2

You've reached the end of your free preview.

Want to read all 3 pages?

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

Stuck? We have tutors online 24/7 who can help you get unstuck.
A+ icon
Ask Expert Tutors You can ask You can ask You can ask (will expire )
Answers in as fast as 15 minutes