An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter B.5, Problem 18P
To determine
To Draw: The sine wave graph for the function
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Students have asked these similar questions
Consider the "step" potential:
V(x) =
(a) Calculate the reflection coefficient, for the case E 0.
(b) Calculate the reflection coefficient for the case E > Vo.
(c) For a potential such as this, which does not go back to zero to the right of
the barrier, the transmission coefficient is not simply |F12/A2 (with A the
-Vo
AV(x)
Scattering from a "cliff"
incident amplitude and F the transmitted amplitude), because the transmitted
wave travels at a different speed. Show that
T =
E-Vo F1²
E |A|²
X
for E> Vo. Hint: You can figure it out using Equation
gantly, but less informatively-from the probability current (
What is T, for E Vo, calculate the transmission coefficient for the step potential, and
check that T + R = 1.
Write down the equations and the associated boundary conditions for
solving particle in a 1-D box of dimension L with a finite potential
well, i.e., the potential energy U is zero inside the box, but finite
outside the box. Specifically, U = U₁ for x L. Assuming that particle's energy E is less
than U, what form do the solutions take? Without solving the
problem (feel free to give it a try though), qualitatively compare with
the case with infinitely hard walls by sketching the differences in
wave functions and probability densities and describing the changes
in particle momenta and energy levels (e.g., increasing or decreasing
and why), for a given quantum number.
Legrende polynomials
The amplitude of a stray wave is defined by:
SO) =x
(21+ 1) exp li8,] sen 8, P(cos 8).
INO
Here e is the scattering angle, / is the angular momentum and 6, is the phase shift produced by the
central potential that performs the scattering. The total cross section is:
Show that:
'É4+ 1)sen² 8, .
Chapter B Solutions
An Introduction to Thermal Physics
Ch. B.1 - Sketch an antiderivative of the function ex2.Ch. B.1 - Prob. 2PCh. B.1 - Prob. 3PCh. B.1 - Prob. 4PCh. B.1 - Prob. 5PCh. B.1 - Prob. 6PCh. B.2 - Prob. 7PCh. B.2 - Prob. 8PCh. B.2 - Prob. 9PCh. B.3 - Prob. 10P
Ch. B.3 - Prob. 11PCh. B.3 - Prob. 12PCh. B.3 - Prob. 13PCh. B.4 - Prob. 14PCh. B.4 - Prob. 15PCh. B.4 - Derive a formula for the volume of a d-dimensional...Ch. B.5 - Derive the general integration formulas B.36Ch. B.5 - Prob. 18PCh. B.5 - Prob. 19PCh. B.5 - Evaluate equation B.41 at x=/2, to obtain a famous...Ch. B.5 - Prob. 21PCh. B.5 - Prob. 22P
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