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 These problems will be discussed in the practice session on Friday, 3 Feb 2006) 1. Consider a particle that is confined in a one-dimensional 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 ( 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 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 re-derive them just quote the result.) (c) Use the result of (b) to determine the time-dependent wave function ( x, t ) of the particle....
View Full Document
- Spring '06