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 3.6, Problem 3.25P
To determine
To find the eigenvalues and eigenvectors of the given Hamiltonian for a certain two-level system, and also to find the matrix representing with respect to the given basis.
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Students have asked these similar questions
The Hamiltonian of a certain system is given by
[1
H = ħw|0 0 0
Lo o 1
Two other observables A and B are represented by
i 0
A = a|-i 00
0 1
0 0
[1
B = b|0
2 0
0 2
w, a, b are positive constant.
Suppose the system is initially in the state
2c
lf(0) >=
-c
2c
where c is a real constant. Determine the normalized state |4(t) >.
What are the eigenvectors of B?
Find the expectation values of A and B in the state |(t) >, and hence determine if A and B are
conservative observables
Consider a physical system whose three-dimensional state
space is spanned by the orthonormal basis formed by the three
kets {|e1>, |e2>, |e3>}. In the basis of these three vectors, taken
in this order, the Hamiltonian H^ and the two operators B^ and
D are defined by:
H = ħwo
3 i 0
i 30
0 02
7
B÷bo -i
i 1- i
1+
6
| (0)) =
7
1+i 1 - i
(e₁] (0))
(€₂ (0))
(€3) (0)
0 0 2α
where wo and bo are constants. Also using this ordered basis,
the initial state of the system is given by:
=
D 0 2α
2a 0 -3a
Suppose that the initial state (0)> was left to evolve until t = 0.
Q: Q: State an uncertainty principle for ABAD. Justify your
answer.
A→ times B→ =
What is the angle between A and B?
What is 2B times 3C?
Chapter 3 Solutions
Introduction To Quantum Mechanics
Ch. 3.1 - Prob. 3.1PCh. 3.1 - Prob. 3.2PCh. 3.2 - Prob. 3.3PCh. 3.2 - Prob. 3.4PCh. 3.2 - Prob. 3.5PCh. 3.2 - Prob. 3.6PCh. 3.3 - Prob. 3.7PCh. 3.3 - Prob. 3.8PCh. 3.3 - Prob. 3.9PCh. 3.3 - Prob. 3.10P
Ch. 3.4 - Prob. 3.11PCh. 3.4 - Prob. 3.12PCh. 3.4 - Prob. 3.13PCh. 3.5 - Prob. 3.14PCh. 3.5 - Prob. 3.15PCh. 3.5 - Prob. 3.16PCh. 3.5 - Prob. 3.17PCh. 3.5 - Prob. 3.18PCh. 3.5 - Prob. 3.19PCh. 3.5 - Prob. 3.20PCh. 3.5 - Prob. 3.21PCh. 3.5 - Prob. 3.22PCh. 3.6 - Prob. 3.23PCh. 3.6 - Prob. 3.24PCh. 3.6 - Prob. 3.25PCh. 3.6 - Prob. 3.26PCh. 3.6 - Prob. 3.27PCh. 3.6 - Prob. 3.28PCh. 3.6 - Prob. 3.29PCh. 3.6 - Prob. 3.30PCh. 3 - Prob. 3.31PCh. 3 - Prob. 3.32PCh. 3 - Prob. 3.33PCh. 3 - Prob. 3.34PCh. 3 - Prob. 3.35PCh. 3 - Prob. 3.36PCh. 3 - Prob. 3.37PCh. 3 - Prob. 3.38PCh. 3 - Prob. 3.39PCh. 3 - Prob. 3.40PCh. 3 - Prob. 3.41PCh. 3 - Prob. 3.42PCh. 3 - Prob. 3.43PCh. 3 - Prob. 3.44PCh. 3 - Prob. 3.45PCh. 3 - Prob. 3.47PCh. 3 - Prob. 3.48P
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