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Essential Quantum Mechanics$
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Gary Bowman

Print publication date: 2007

Print ISBN-13: 9780199228928

Published to Oxford Scholarship Online: January 2008

DOI: 10.1093/acprof:oso/9780199228928.001.0001

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Angular Momentum

Angular Momentum

(p.95) 8 Angular Momentum
Essential Quantum Mechanics

Gary E. Bowman

Oxford University Press

Angular momentum is one of the more abstract topics in quantum mechanics. This chapter begins with a review of classical angular momentum. Quantum-mechanical angular momentum is then introduced by obtaining operators from their classical counterparts. The commutation relations amongst those operators and the corresponding uncertainty relations then follow. Eigenstates and eigenvalues of the angular momentum operators are then introduced (but not derived). From these follow the raising and lowering operators. Physical meaning is imparted to quantum angular momentum by considering predictions for sequential measurements, and by comparing the conceptual pictures of angular momentum in classical and quantum mechanics. Finally, quantum spin and orbital angular momenta, and the deep differences between them, are discussed.

Keywords:   commutation relations, uncertainty relations, raising operator, lowering operator, measurement, spin angular momentum, orbital angular momentum

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