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 3.6, Problem 3.30P
To determine
The transformation from position space to energy space wave function for a discrete spectrum with time independent potential.
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Students have asked these similar questions
A particle with mass m is moving along the x-axis in a potential given by the potential energy
function U(x) = 0.5mw²x². Compute the product (x, t)*U (x) V (x, t). Express your
answer in terms of the time-independent wave function, (x).
Consider the particle in the infinite potential well as shown in Figure P2.29. Derive
and sketch the wave functions corresponding to the four lowest energy levels. (Do not
normalize the wave functions.)
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.
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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