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9 - Particle in a Central Potential; Orbital Angular Momentum

Published online by Cambridge University Press:  05 December 2024

Rocco Schiavilla
Affiliation:
Old Dominion University, Virginia
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Summary

The orbital angular momentum operator is defined and its commutation relations with the position and momentum operators, and generally with vector operators, are obtained; the relationship between the square of the momentum operator and the square of the orbital angular momentum is derived; the spectrum of the square and z-component of the orbital angular momentum is obtained by solving the Schröedinger equation near the origin; the radial equation is derived and the spherical harmonics are obtained as solutions of the associated Legendre equation.

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Chapter
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Quantum Mechanics through Problems
With Complete Solutions
, pp. 270 - 290
Publisher: Cambridge University Press
Print publication year: 2024

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