Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Question
Chapter 12.3, Problem 12.4P
(a)
To determine
The proof of the properties 12.17, 12.18, 12.19, and 12.20.
(b)
To determine
Show that the time evolution of the density operator is governed by the equation,
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Students have asked these similar questions
Consider the function
v(1,2) =(
[1s(1) 3s(2) + 3s(1) 1s(2)]
[x(1) B(2) + B(1) a(2)]
Which of the following statements is incorrect concerning p(1,2) ?
a.
W(1,2) is normalized.
Ob.
The function W(1,2) is symmetric with respect to the exchange of the space and the spin coordinates of the two electrons.
OC.
y(1,2) is an eigenfunction of the reference (or zero-order) Hamiltonian (in which the electron-electron repulsion term is ignored) of Li with
eigenvalue = -5 hartree.
d.
The function y(1,2) is an acceptable wave function to describe the properties of one of the excited states of Lit.
Oe.
The function 4(1,2) is an eigenfunction of the operator S,(1,2) = S;(1) + S,(2) with eigenvalue zero.
In free space, U (r, t)
must satisfy tne wave equation, VU - (1/)U/at = 0. Use the definition (12.1-21) to show
that the mutual coherence function G(r1,r2, 7) satisfies a pair of partial differential cquations known
as the Wolf equations,
1 PG
= 0
vG –
(12.1-24a)
vG -
1 G
= 0,
(12.1-24b)
where V and V are the Laplacian operators with respect to r, and r2, respectively.
G(rı, r2, 7) = (U*(r1,t) U(r2, t + T)).
(12.1-21)
Mutual Coherence Function
Prove the following commutator identity:
[AB, C] = A[B. C]+[A. C]B.
Chapter 12 Solutions
Introduction To Quantum Mechanics
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