4604_ProblemSet3

# 4604_ProblemSet3 - PHY4604 Problem Set 3 PHY 4604 Problem...

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

PHY4604 Problem Set 3 Department of Physics Page 1 of 2 PHY 4604 Problem Set #3 Due Monday October 2, 2006 (in class) (Total Points = 130, Late homework = 50%) Reading: Griffiths Chapter 2 (sections 2.4, 2.5, and 2.6). Useful Math: ) ( 2 1 2 1 2 / ) 1 ( 0 2 + + Γ = n n ax n a dx e x , where Γ (x) is the gamma function and Γ (x+1) = x Γ (x) . Γ (1) = Γ (2) = 1, Γ (n) = (n-1)! if n is a positive integer, and π = Γ ) ( 2 1 . Hence, a dx e ax = +∞ 2 and 4 / 4 / ) 2 / ( ) ( 2 2 2 2 ab ab b x a bx x a e a dx e e dx e = = +∞ + +∞ + . Problem 1 (40 points): A free particle has a Gaussian initial wave function given by 2 ) 0 , ( ax Ae x = Ψ , where A and a are positive real constants. (a) (2 points) Find the value of A that normalizes this wave function such that 1 ) 0 , ( ) 0 , ( = Ψ Ψ +∞ dx x x . (b) (8 points) Find ) , ( t x Ψ . (c) (8 point) Compute the probability density 2 | ) , ( | ) , ( t x t x Ψ = ρ . Express your answer in terms of the time dependent quantity 2 ) / 2 ( 1 m at a w h + . Sketch

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 04/19/2008 for the course PHY 4604 taught by Professor Field during the Spring '07 term at University of Florida.

### Page1 / 2

4604_ProblemSet3 - PHY4604 Problem Set 3 PHY 4604 Problem...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online