This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Quantum Mechanics Problem Sheet 3 (Solutions are to be handed in for marking before the lecture on Monday, 7 Feb 2005) 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 . The particle is initially distributed uniformly inside the box, so that its wave function at time t = 0 is ( x, 0) = N 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 n ( x ) in the box, ( x, 0) = X n =1 c n n ( x ) , and calculate the expansion coefficients c n . Check your result by sketching ( x, 0), 1 ( x ) , and 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 n ( x ) , you dont need to rederive them just quote the result from your lecture notes or from the previous problem sheet.) (c) Use the result of (b) to determine the timedependent wave function...
View Full
Document
 Spring '02
 POCANIC
 Physics, mechanics

Click to edit the document details