Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 3.3, Problem 3.10P
To determine
The ground state wavefunction of infinite square well is an eigen function of momentum or not. In the case it is an eigen function, the value of momentum.
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An electron in a region of length L is described by the normalized wavefunction ψ(x) = (2/L)1/2sin(2πx/L) in the range x = 0 to x = L; outside this range the wavefunction is zero. Evaluate ⟨x⟩. The necessary integrals will be found in the Resource section.
Problem 2.15 In the ground state of the harmonic oscillator, what is the probability
(correct to three significant digits) of finding the particle outside the classically
allowed region? Hint: Classically, the energy of an oscillator is E = (1/2)ka² =
(1/2)mw²a², where a is the amplitude. So the "classically allowed region" for an
oscillator of energy E extends from -√2E/mw² to +√2E/mw². Look in a math
table under "Normal Distribution" or "Error Function" for the numerical value of
the integral.
1.4 Show that the distance of closest approach d, in Rutherford scattering leading to an
angle of deflection 0, is given by
d=(1+ cosec 0,2).
where p is detined in Fig. 1.6.
(Use the conservation of energy and angular momentum.]
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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