Chapter6_7 - PHY3063 R. D. Field The Infinite Square Well...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
PHY3063 R. D. Field Department of Physics Chapter6_7.doc University of Florida The Infinite Square Well (1) Particle in a One-Dimensional Box: Consider the solution of ) ( ) ( ) ( ) ( 2 2 2 2 x E x x V dx x d m ψ = + h , where h / ) ( ) , ( iEt e x t x = Ψ , for the case V(x) = if x 0 and V(x) = if x L and V(x) = 0 for 0 < x < L . For x 0 and x L we have 0 ) ( ) ( ) ( ) ( ) ( ) ( 2 2 2 2 = → = + x x x V E x dx x d x mV V h . For 0 < x < L we have ) ( ) ( 2 ) ( 2 2 2 2 x k x mE dx x d = = h where 2 2 h mE k = . The most general solution is ikx ikx Be Ae x + = ) ( where A and B are constants. Boundary Conditions: We require that ψ (x) be “square-integrable” and that it be continuous and “single valued”. Thus at x = 0 0 ) 0 ( = + = = B A x and hence ) sin( 2 ) ( ) ( kx iA e e A x ikx ikx = = . At x = L we have 0 ) sin( 2 ) ( = = = kL iA L x which implies that kL = n π with n = 1, 2, 3,. .. Energy Levels: We see that only certain values of k are allowed which means that only the following energies are allowed: 0 2
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/29/2011 for the course PHY 3063 taught by Professor Field during the Spring '07 term at University of Florida.

Ask a homework question - tutors are online