Solution Manual for Modern Quantum Mechanics, 2nd Edition

Unlock the answers to every textbook problem with Solution Manual for Modern Quantum Mechanics, 2nd Edition, making studying more efficient and effective.

Henry Martinez

Contributor

4.2

7 months ago

Preview (16 of 112 Pages)

100%

Purchase to unlock

Solution Manual for Modern Quantum Mechanics, 2nd Edition - Page 1 preview image

Loading page ...

2Chapter One1.AC{D, B}=ACDB+ACBD,A{C, B}D=ACBD+ABCD,C{D, A}B=CDAB+CADB, and{C, A}DB=CADB+ACDB. Therefore−AC{D, B}+A{C, B}D−C{D, A}B+{C, A}DB=−ACDB+ABCD−CDAB+ACDB=ABCD−CDAB= [AB, CD]In preparing this solution manual, I have realized that problems 2 and 3 in are misplacedin this chapter. They belong in Chapter Three. The Pauli matrices are not even defined inChapter One, nor is the math used in previous solution manual.– Jim Napolitano2.(a)Tr(X) =a0Tr(1) +Tr(σ)a= 2a0sinceTr(σ) = 0. AlsoTr(σkX) =a0Tr(σk) +Tr(σkσ)a=12Tr(σkσ+σσk)a=δkTr(1)a= 2ak. So,a0=12Tr(X) andak=12Tr(σkX).(b) Just do the algebra to finda0= (X11+X22)/2,a1= (X12+X21)/2,a2=i(−X21+X12)/2, anda3= (X11−X22)/2.3.Since det(σ·a) =−a2z−(a2x+a2y) =−|a|2, the cognoscenti realize that this problemreally has to do with rotation operators. From this result, and (3.2.44), we writedetexp±iσ·ˆnφ2= cosφ2±isinφ2and multiplying out determinants makes it clear that det(σ·a) = det(σ·a). Similarly, use(3.2.44) to explicitly write out the matrixσ·aand equate the elements to those ofσ·a.With ˆnin thez-direction, it is clear that we have just performed a rotation (of the spinvector) through the angleφ.4.(a)Tr(XY)≡aa|XY|a=aba|X|bb|Y|aby inserting the identity operator.Then commute and reverse, soTr(XY) =bab|Y|aa|X|b=bb|Y X|b=Tr(Y X).(b)XY|α=X[Y|α] is dual toα|(XY)†, butY|α ≡|βis dual toα|Y†≡ β|andX|βis dual toβ|X†so thatX[Y|α] is dual toα|Y†X†. Therefore (XY)†=Y†X†.(c) exp[if(A)] =aexp[if(A)]|aa|=aexp[if(a)]|aa|(d)aψ∗a(x)ψa(x) =ax|a∗x|a=ax|aa|x=x|x=δ(x−x)5.For basis kets|ai, matrix elements ofX≡|αβ|areXij=ai|αβ|aj=ai|αaj|β∗.For spin-1/2 in the| ±zbasis,+|Sz= ¯h/2= 1,−|Sz= ¯h/2= 0, and, using (1.4.17a),±|Sx= ¯h/2= 1/√2. Therefore|Sz= ¯h/2Sx= ¯h/2|.=1√211006.A[|i+|j] =ai|i+aj|j = [|i+|j] so in general it is not an eigenvector, unlessai=aj.That is,|i+|jis not an eigenvector ofAunless the eigenvalues are degenerate.

Preview Mode

This document has 112 pages. Sign in to access the full document!

Report

Study Now!

XY-Copilot AI

Unlimited Access

Secure Payment

Instant Access

24/7 Support

Document Chat

Document Details

Subject

Physics

Textbook

Modern Quantum Mechanics by J. J. S...

Solution Manual for Modern Quantum Mechanics, 2nd Edition

Study Now!

Document Details

Related Documents

Exploring Light Intensity Through Polarizers

IPL Lab Report

Distance Time Velocity Gizmo Handout-2

Energy Skate Park Activity

Exploring Density Measuring Mass and Volume of Obj

Student Exploration Distance Time Graphs

Barron's Physics Practice Plus: 400+ Online Questions and Quick Study Review (2022)

College Physics: A Strategic Approach, 4th Edition Test Bank

Test Bank for Conceptual Integrated Science, 3rd Edition

Practical Applications Of Density Calculations In Everyday Scenarios

Company

Explore

Study Tools