Angular momentum, g-value, and magnetic flux of gyration states
Two of the world's leading (Nobel laureate) physicists disagree on the definition of the orbital angular momentum L of the Landau gyration states of a spinless charged particle in a uniform external magnetic field B = B i{sub Z}. According to Richard P. Feynman (and also Frank Wilczek) L = (rx{mu}v) = rx(p - qA/c), while Felix Bloch (and also Kerson Huang) defines it as L = rxp. We show here that Bloch's definition is the correct one since it satisfies the necessary and sufficient condition LxL = i{Dirac h} L, while Feynman's definition does not. However, as a consequence of the quantized Aharonov-Bohm magnetic flux, this canonical orbital angular momentum (surprisingly enough) takes half-odd-integral values with a zero-point gyration states of L{sub Z} = {Dirac h}/2. Further, since the diamagnetic and the paramagnetic contributions to the magnetic moment are interdependent, the g-value of these gyration states is two and not one, again a surprising result for a spinless case. The differences between the gauge invariance in classical and quantum mechanics, Onsager's suggestion that the flux quantization might be an intrinsic property of the electromagnetic field-charged particle interaction, the possibility that the experimentally measured fundamental unit of the flux quantum need not necessarily imply the existence of electron pairing'' of the Bardeen-Cooper-Schrieffer superconductivity theory, and the relationship to the Dirac's angular momentum quantization condition for the magnetic monopole-charged particle composites (i.e. Schwinger's dyons), are also briefly examined from a pedestrian viewpoint.
- Research Organization:
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Sponsoring Organization:
- USDOE; USDOE, Washington, DC (United States)
- DOE Contract Number:
- AC02-76CH03073
- OSTI ID:
- 5125808
- Report Number(s):
- PPPL-2792; ON: DE92001932
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EXCITED STATES
GYROMAGNETIC RATIO
MAGNETIC FLUX
ORBITAL ANGULAR MOMENTUM
HAMILTONIANS
LAGRANGIAN FUNCTION
MAGNETIC FIELDS
MAGNETIC MOMENTS
MONOPOLES
ANGULAR MOMENTUM
ENERGY LEVELS
FUNCTIONS
MATHEMATICAL OPERATORS
QUANTUM OPERATORS
700103* - Fusion Energy- Plasma Research- Kinetics
657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics