Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 7, Problem 7.49P
To determine
Prove the relation
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Problem #1
(Problem 5.3 in book). Come up with a function for A (the Helmholtz free energy) and
derive the differential form that reveals A as a potential:
dA < -SdT – pdV [Eqn 5.20]
Problem 9.4
For the 2D LHO with K1 = K2 show that
and
[ê, ²] = 2ihxy,
(ê, p}] = -2ihxy
Problem 9.5
It follows from the above that
[ê., Ĥ] = 0
if K1 = K2 only
Work out the equivalent commutator for ê and é, with the
Hamiltonian. What do these mean?
Problem 6.25 Express the expectation value of the dipole moment pe for an electron in the
hydrogen state
1
4 =
(211 +210)
√2
in terms of a single reduced matrix element, and evaluate the expectation value. Note: this
is the expectation value of a vector so you need to compute all three components. Don't
forget Laporte's rule!
Chapter 7 Solutions
Introduction To Quantum Mechanics
Ch. 7.1 - Prob. 7.1PCh. 7.1 - Prob. 7.2PCh. 7.1 - Prob. 7.3PCh. 7.1 - Prob. 7.4PCh. 7.1 - Prob. 7.5PCh. 7.1 - Prob. 7.6PCh. 7.2 - Prob. 7.8PCh. 7.2 - Prob. 7.9PCh. 7.2 - Prob. 7.10PCh. 7.2 - Prob. 7.11P
Ch. 7.2 - Prob. 7.12PCh. 7.2 - Prob. 7.13PCh. 7.3 - Prob. 7.15PCh. 7.3 - Prob. 7.16PCh. 7.3 - Prob. 7.17PCh. 7.3 - Prob. 7.18PCh. 7.3 - Prob. 7.19PCh. 7.3 - Prob. 7.20PCh. 7.3 - Prob. 7.21PCh. 7.3 - Prob. 7.22PCh. 7.4 - Prob. 7.23PCh. 7.4 - Prob. 7.24PCh. 7.4 - Prob. 7.25PCh. 7.4 - Prob. 7.26PCh. 7.4 - Prob. 7.27PCh. 7.4 - Prob. 7.28PCh. 7.4 - Prob. 7.29PCh. 7.5 - Prob. 7.31PCh. 7.5 - Prob. 7.32PCh. 7 - Prob. 7.33PCh. 7 - Prob. 7.34PCh. 7 - Prob. 7.35PCh. 7 - Prob. 7.36PCh. 7 - Prob. 7.37PCh. 7 - Prob. 7.38PCh. 7 - Prob. 7.39PCh. 7 - Prob. 7.40PCh. 7 - Prob. 7.42PCh. 7 - Prob. 7.43PCh. 7 - Prob. 7.44PCh. 7 - Prob. 7.45PCh. 7 - Prob. 7.46PCh. 7 - Prob. 7.47PCh. 7 - Prob. 7.49PCh. 7 - Prob. 7.50PCh. 7 - Prob. 7.51PCh. 7 - Prob. 7.52PCh. 7 - Prob. 7.54PCh. 7 - Prob. 7.56PCh. 7 - Prob. 7.57P
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- The Hamilton function for a point particle moving in a central potential is given by p? H + a|x|". 2m Consider the vector A = p x L+ ma where L is the angular momentum of the particle. (a) Calculate the Poisson bracket {H, Ar}, where A is the k-th component of the vector A. (b) Determine the value of the exponent n for which the vector A becomes a conserved quantity.arrow_forwardDerive Eq.(7.13) by using set of equations (7.2 a,b,c and d).arrow_forwardFor Problem 8.37, how do I find <1/r> within the integral? I think that the exponent function inside of P(r) is actually troublesome to finding what I need to find; however, I am not certain of what's really the correct procedure here.arrow_forward
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