Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 2.3, Problem 2.15P
To determine

The H5(ξ) and H6(ξ) by using the recursion formula.

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Draw a diagram
Imagine two concentric cylinders, centered on the vertical axis, with radii R± ε, where ε is very small. A small frictionless puck of thickness 2ε is inserted between the two cylinders, so that it can be considered a point mass that can move freely at a fixed distance from the vertical axis. If we use cylindrical polar coordinates (p, op, z) for its position (Problem 1.47), then p is fixed at p = R, while op and z can vary at will. Write down and solve Newton's second law for the general motion of the puck, including the effects of gravity. Describe the puck's motion.
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