This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Quantum Mechanics Problem Sheet 3 These problems will be discussed in the practice session on Friday, 3 Feb 2006) 1. Consider a particle that is confined in a onedimensional box, ie in a potential V ( x ) = for 0 ≤ x ≤ L ∞ for x < 0 and x > L . Its initial wave function at time t = 0 is ψ ( x, 0) = N x L 2 for 0 ≤ x ≤ L for x < 0 and x > L . (a) Determine the normalization constant N . (b) Write the initial wave function as a superposition of the stationary states φ n ( x ) in the box, ψ ( x, 0) = ∞ X n =1 c n φ n ( x ) , and calculate the expansion coefficients c n . Check your result by sketching ψ ( x, 0), φ 1 ( x ) , and φ 2 ( x ) and considering the symmetry of these functions around the middle of the box. (If you have understood how one gets the stationary states φ n ( x ) , you don’t need to rederive them — just quote the result.) (c) Use the result of (b) to determine the timedependent wave function ψ ( x, t ) of the particle....
View
Full
Document
This note was uploaded on 04/07/2008 for the course PHYS F3026 taught by Professor Eberlein during the Spring '06 term at Uni. Sussex.
 Spring '06
 EBERLEIN
 mechanics

Click to edit the document details