Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 6.8, Problem 6.26P
To determine
Work out the value of
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Q4.1 Determine explicitly (i.e. give all the details of the derivation), the energy eigenvalues En
and the normalised energy eigenfunctions {on (x)} for a particle moving in a one dimensional 'box'
where the potential energy is U (x) = 0 for 0 a.
Consider two particles m1 and m2. Let mlbe confined to move on a circle of radius R1
in the z-0 plane and centered at x-0, y-0. Let m2 be confined to move on a circle of
radius R2 in the z-a plane and centered at x-0, y-0. A massless spring of spring
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Set up the Lagrangian for the system.
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Set up the Lagrange equations using Lagrange multipliers.
Q4.1 Determine explicitly (i.e. give all the details of the derivation), the energy eigenvalues En
and the normalised energy eigenfunctions {n (x)} for a particle moving in a one dimensional 'box'
where the potential energy is U (x) = 0 for 0 a.
Show that the average or mean value for the position x of a particle in a state represented by the
nth eigenfunction is
a
If the particle's wavefunction is represented by the eigenfunction øn (x), find an integral expression
for the probability of finding the particle somewhere in the interval b
Chapter 6 Solutions
Introduction To Quantum Mechanics
Ch. 6.1 - Prob. 6.1PCh. 6.2 - Prob. 6.2PCh. 6.2 - Prob. 6.3PCh. 6.2 - Prob. 6.4PCh. 6.2 - Prob. 6.5PCh. 6.2 - Prob. 6.7PCh. 6.4 - Prob. 6.8PCh. 6.4 - Prob. 6.9PCh. 6.4 - Prob. 6.10PCh. 6.4 - Prob. 6.11P
Ch. 6.4 - Prob. 6.12PCh. 6.4 - Prob. 6.13PCh. 6.5 - Prob. 6.14PCh. 6.5 - Prob. 6.15PCh. 6.5 - Prob. 6.16PCh. 6.5 - Prob. 6.17PCh. 6.6 - Prob. 6.18PCh. 6.6 - Prob. 6.19PCh. 6.7 - Prob. 6.20PCh. 6.7 - Prob. 6.21PCh. 6.7 - Prob. 6.22PCh. 6.7 - Prob. 6.23PCh. 6.7 - Prob. 6.25PCh. 6.8 - Prob. 6.26PCh. 6.8 - Prob. 6.27PCh. 6.8 - Prob. 6.28PCh. 6.8 - Prob. 6.30PCh. 6 - Prob. 6.31PCh. 6 - Prob. 6.32PCh. 6 - Prob. 6.34PCh. 6 - Prob. 6.35PCh. 6 - Prob. 6.36PCh. 6 - Prob. 6.37P
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