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, Problem 3.44P
(a)
To determine
The value of state
(b)
To determine
The value of state
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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.
Two particles, each of mass m, are connected by a light inflexible string of length l. The string passes through a small smooth hole in the centre of a smooth horizontal table, so that one particle is below the table and the other can move on the surface of the table. Take the origin of the (plane) polar coordinates to be the hole, and describe the height of the lower particle by the coordinate z, measured downwards from the table surface.
Here, the total force acting on the mass which is on the table is -T r^ (r hat). Why?
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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