Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Chapter 7, Problem 63E
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A spin state of an electron in the vector form is given by
3i
X = A
4
%3D
(a) Determine the normalization constant A, assuming it to be real and positive.
(b) Write down the x using the X+ and X-. If z-component of the spin of the electron is
measured, what is the probability of finding the value in +ħ/2?
(c) Determine the expectation value and uncertainty of S? in terms of h when the electron
is in spin state x. Justify your answer.
(d) Determine the expectation value of the product S?S, in terms of h when the electron
is in spin state X.
In a one-dimensional system, the density of states is given by N(E)= 2m, where L is the length of the sample
L√2m
in the
and m is the mass of the electron, as seen in class. There are N quantum particles with spin |S| =
sample (the quantum particles can be understood as 'special electrons with spin [S] ='), so that each state can
be occupied by 2|S| + 1 particles. Determine the Fermi energy at 0 K.
Consider a crystal containing N identical atoms. As a crude approximation, assume that each atom is under the
effect of a 3D harmonic potential which keeps it localized, and that atoms do not interact with each other. We
have therefore 3N simple quantum harmonic oscillators, all of them with the same angular frequency w, that do
not interact with each other. Recall that each harmonic oscillator has the energy levels En = ħw(n + 1/{ ),
0, 1, 2, .
n =
(a)
Compute the canonical partition function Q(T, N), the free energy A(T, N), the internal energy
E(T, N), the heat capacity C(T, N), and the entropy S(T, N) for the Einstein solid.
Chapter 7 Solutions
Modern Physics
Ch. 7 - Prob. 1CQCh. 7 - Prob. 2CQCh. 7 - Prob. 3CQCh. 7 - Prob. 4CQCh. 7 - Prob. 5CQCh. 7 - Prob. 6CQCh. 7 - Prob. 7CQCh. 7 - Prob. 8CQCh. 7 - Prob. 9CQCh. 7 - What are the dimensions of the spherical harmonics...
Ch. 7 - Prob. 11CQCh. 7 - Prob. 12CQCh. 7 - Prob. 13CQCh. 7 - Prob. 14CQCh. 7 - Prob. 15CQCh. 7 - Prob. 16CQCh. 7 - Prob. 17ECh. 7 - Prob. 18ECh. 7 - Prob. 19ECh. 7 - Prob. 20ECh. 7 - Prob. 21ECh. 7 - Prob. 22ECh. 7 - Prob. 23ECh. 7 - Prob. 24ECh. 7 - Prob. 25ECh. 7 - Prob. 26ECh. 7 - Prob. 27ECh. 7 - Show that of hydrogen’s spectral seriesLyman,...Ch. 7 - Prob. 29ECh. 7 - Prob. 30ECh. 7 - Prob. 31ECh. 7 - Prob. 32ECh. 7 - Prob. 33ECh. 7 - Prob. 34ECh. 7 - Prob. 35ECh. 7 - Prob. 36ECh. 7 - Prob. 37ECh. 7 - A particle orbiting due to an attractive central...Ch. 7 - Prob. 39ECh. 7 - Prob. 40ECh. 7 - Prob. 41ECh. 7 - Prob. 42ECh. 7 - Prob. 43ECh. 7 - How many different 3d states are there? What...Ch. 7 - Prob. 45ECh. 7 - Prob. 46ECh. 7 - Prob. 47ECh. 7 - Prob. 48ECh. 7 - Prob. 49ECh. 7 - Prob. 50ECh. 7 - Prob. 51ECh. 7 - Prob. 52ECh. 7 - Prob. 53ECh. 7 - Prob. 54ECh. 7 - For states where l=n1 , the radial probability...Ch. 7 - Prob. 56ECh. 7 - Prob. 57ECh. 7 - Prob. 58ECh. 7 - Prob. 59ECh. 7 - Prob. 60ECh. 7 - Prob. 61ECh. 7 - Prob. 62ECh. 7 - Prob. 63ECh. 7 - Prob. 64ECh. 7 - Prob. 65ECh. 7 - Prob. 66ECh. 7 - Prob. 67ECh. 7 - Prob. 68ECh. 7 - Prob. 69ECh. 7 - Prob. 70ECh. 7 - Prob. 71ECh. 7 - Prob. 72ECh. 7 - Prob. 73ECh. 7 - Prob. 74ECh. 7 - Prob. 75ECh. 7 - Prob. 76ECh. 7 - Prob. 77ECh. 7 - Prob. 78ECh. 7 - Prob. 79CECh. 7 - Prob. 80CECh. 7 - Prob. 81CECh. 7 - Prob. 83CECh. 7 - Prob. 84CECh. 7 - Prob. 85CECh. 7 - Prob. 86CECh. 7 - Prob. 87CECh. 7 - Prob. 89CE
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