ps03 - Quantum Mechanics Problem Sheet 3 (Solutions are to...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the 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 one-dimensional 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 re-derive them just quote the result from your lecture notes or from the previous problem sheet.) (c) Use the result of (b) to determine the time-dependent wave function...
View Full Document

Page1 / 2

ps03 - Quantum Mechanics Problem Sheet 3 (Solutions are to...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online