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: Chem 3890 Physical Chemistry I Fall 2010 Chemistry 3890 Problem Set 4 Fall 2010 Due: in class, Friday, October 1 Last revised: September 24, 2010 Problem 1 A PIB is prepared in the state ( x, t = 0) = ( x ) = bracketleftBig 2 1 ( x )- i 2 ( x ) + e i/ 4 2 3 ( x ) bracketrightBig , (1) at t = 0, where the particle has mass m , 0 x a and the are the usual PIB eigenfunctions. 1. Normalize the state ( x ). Use the normalized ( x ) in the rest of the problem. 2. The particle energy (Hamiltonian H ) is measured at t = 0. What is the probability of finding E = E 1 , E = E 2 , E = E 3 and E = E 4 , respectively, in an individual measurement of H ? 3. If a large number of such measurements are made, calculate the expectation values ( H ) and ( H 2 ) , and the associated uncertainty H . 4. Write down an expression for the probability P ( ) that a PIB in state ( x ) will be found in the range 0 x when the particle position is measured; leave your expression in the form of an integral involving and * . Use Mathematica to evaluate your expression for P ( ) for the state (1)....
View Full Document