3890ps6_10 - Chem 3890 Physical Chemistry I Fall 2010...

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: Chem 3890 Physical Chemistry I Fall 2010 Chemistry 3890 Problem Set 6 Fall 2010 Due: in class, Friday, October 22 Last revised: October 16, 2010 Additions/corrections: Problem 1 Consider two quantum mechanical operators A and B , with A i = i i and B j = j j . Take A and B to be Hermitian, so that the respective eigenstates are orthonormal, integraldisplay d x * i i prime = i,i prime (1a) integraldisplay d x * j j prime = j,j prime . (1b) Also, assume that neither operator has degenerate eigenvalues, so that i negationslash = i prime for i negationslash = i prime , and j negationslash = j prime for j negationslash = j prime . Normalized functions i and j are related by the expressions: 1 = 1 2 1 + 1 2 2- 1 2 3 2 =- 1 2 1 + 1 2 2 3 = 1 2 1 + 1 2 2 + 1 2 3 (2) 1. Using only the orthonormality of the states j , and the relations (2), verify that the states i are in fact orthonormal. 2. Find expressions for the j in terms of the i . That is, determine the coefficients c ij in the expansion j = 3 summationdisplay i =1 i c ij , j = 1 , 2 , 3 (3) To determine these coefficients, note that you can use the orthonormality of the j to determine the integrals ( j | i ) integraltext d x * j i , and that ( | ) = integraldisplay d x * ( x ) ( x ) = bracketleftbiggintegraldisplay d x * ( x ) ( x ) bracketrightbigg * = ( | ) * . (4) 3. If a particle is initially in the state = 1 3 [ 1 + i 2- 3 ] , (5) what is the probability that a measurement of the dynamical variable represented by...
View Full Document

This note was uploaded on 08/25/2011 for the course CHEM 3890 at Cornell University (Engineering School).

Page1 / 3

3890ps6_10 - Chem 3890 Physical Chemistry I Fall 2010...

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