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 11, Problem 11.24P
(a)
To determine
Generalize the wave function for time dependent perturbation to find the coefficients for time dependent perturbation.
(b)
To determine
The coefficients
(c)
To determine
The probability of transition for a constant perturbation turned on after some time.
(d)
To determine
The transition probability for a sinusoidal perturbation.
(e)
To determine
The transition rate for stimulated emission for a multi-level system immersed in incoherent
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Students have asked these similar questions
The Hamiltonian of an electron of mass m in a constant electric field E in one dimension can be written as Ĥ=+eEx where â and are the position and momentum operators,
respectively. With initials conditions (t = 0) = 0 and p(t = 0) = 0, which one of the following gives (t) at time in the Heisenberg picture? You may use the commutator
[â,p] = iħ.
O a.
O b.
eEt2
2m
O C. e Et
O d. -eEt
O e.
eEt²
m
pt
m
Verify that the two eigenvectors in (11.8) are perpendicular, and that C in (11.10) satisfies the condition (7.9) for an orthogonal matrix.
The Hamiltonian of a certain system is given by
[1 0
H = ħw]0
LO 0
1
Two other observables A and B are represented by
1 0 0
, B = b]0 2 0
lo o
0-
i 0
A = a|-i 0 0
0 1
w, a, b are positive constant.
a. Find the eigenvalues and normalized eigenvectors of H
b. Suppose the system is initially in the state
2c
lµ(0) >=
-c
2c
where c is a real constant. Determine the normalized state |(t) >.
c. What are the eigenvectors of B?
d. Find the expectation values of A and B in the state |p(t) >, and hence determine if A and B are
conservative observables
Chapter 11 Solutions
Introduction To Quantum Mechanics
Ch. 11.1 - Prob. 11.1PCh. 11.1 - Prob. 11.2PCh. 11.1 - Prob. 11.3PCh. 11.1 - Prob. 11.4PCh. 11.1 - Prob. 11.5PCh. 11.1 - Prob. 11.6PCh. 11.1 - Prob. 11.7PCh. 11.1 - Prob. 11.8PCh. 11.1 - Prob. 11.9PCh. 11.3 - Prob. 11.10P
Ch. 11.3 - Prob. 11.11PCh. 11.3 - Prob. 11.12PCh. 11.3 - Prob. 11.13PCh. 11.3 - Prob. 11.14PCh. 11.3 - Prob. 11.15PCh. 11.3 - Prob. 11.16PCh. 11.4 - Prob. 11.17PCh. 11.5 - Prob. 11.18PCh. 11.5 - Prob. 11.19PCh. 11.5 - Prob. 11.20PCh. 11.5 - Prob. 11.21PCh. 11.5 - Prob. 11.22PCh. 11 - Prob. 11.23PCh. 11 - Prob. 11.24PCh. 11 - Prob. 11.25PCh. 11 - Prob. 11.26PCh. 11 - Prob. 11.27PCh. 11 - Prob. 11.28PCh. 11 - Prob. 11.29PCh. 11 - Prob. 11.30PCh. 11 - Prob. 11.31PCh. 11 - Prob. 11.33PCh. 11 - Prob. 11.35PCh. 11 - Prob. 11.36PCh. 11 - Prob. 11.37P
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