quiz01sol

# quiz01sol - ECE 4060 Introduction to Quantum and...

This preview shows pages 1–3. Sign up to view the full content.

ECE 4060: Introduction to Quantum and Statistical Mechanics Quiz 1 Solution Prob. 1. Given a wave function of a free particle at t = 0 as: ( 29 ( 29 - = otherwise x x ik A x 0 1 1 exp 0 , 0 ψ (a) Find A . (5 pts) By normalization requirement of = 1 * dx ψ ψ , 2 1 = A . (b) Graphically illustrate ( 29 ( 29 2 0 , 0 , x x P = and Re ( (x,0)), assuming 0 < k 0 < 1. (10 pts) (c) Assuming a dispersion relation of m k 2 2 G = ϖ , graphically illustrate P(x, t) and Re ( (x,t)) (10 pts) (*** Due to a critical error in Homework 2, this problem will not count. ***) Prob. 2. Given a wave function of a free particle at t = 0 as: ( 29 ( 29 ( 29 2 1 2 1 exp 2 1 exp 2 3 0 , k k x ik x ik x + = 1 P(x,0) Re ( (x,0)) x x P(x,t) Re ( (x,t)) x x 1/2 1 - 1 1 1 2 / 1

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

View Full Document
(a) What is the expectation value of momentum p ˆ at t = 0 ? (10 pts) 2 1 4 1 4 3 | ˆ | k k p + = ψ (b) If we measure the momentum at t = 0 , what are the possible outcome? What are the probabilities of obtaining those outcome? Briefly explain.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

quiz01sol - ECE 4060 Introduction to Quantum and...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online