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 3.2, Problem 3.4P
(a)
To determine
Show that the sum of two hermition operator is hermition.
(b)
To determine
The condition for
(c)
To determine
The condition for the two product of two hermition operator is hermition.
(d)
To determine
Show that the position and Hamiltonian operator are hermition.
Expert Solution & Answer
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Students have asked these similar questions
Evaluate the commutator [Â,B̂] of the following operators.
Show that the operator
H = -1/2(d^2/dx^2)
is hermitian, assuming that it operates on a Hilbert space of L^2 functions whose functions and derivatives vanish at x = −∞ and x = +∞
Consider a particle of spin s = 3/2.
(a) Find the matrices representing the operators S^
x
, S^
y
,S^
z
,
^
Sx
2
and ^
S y
2 within the basis of
^
S
2
and S^
z
(b) Find the energy levels of this particle when its Hamiltonian is given by
^H=
ϵ 0
h
2
( Sx
2−S y
2
)−
ϵ 0
h
( S^
Z )
where ϵ 0
is a constant having the dimensions of energy. Are these levels degenerate?
(c) If the system was initially in an eigenstate Ψ0=(
1
0
0
0)
, find the state of the system at time
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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