Abstract
The consequences of Dirac's quantization condition are discussed. Observing that this condition generally leads to contradiction and that the normal explanation to resolve the contradiction seems unsatisfactory, we propose a modified quantization condition. It is shown that operator ordering ambiguity could be represented as the arbitrariness of the distribution functions in the modified condition.
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References
N. Woodhouse,Geometric Quantization (Oxford University Press, New York, 1980); J. Sniatycki,Geometric Quantization and Quantum Mechanics (Springer, New York, 1980).
C. J. Isham, inRelativity, Groups and Topology II, B. S. DeWitt and R. Stora, eds. (Elsevier Science Publisher, New York, 1984).
For discussions on operator-ordering problem and various ordering rules, see the following papers and references therein: J. R. Shewell,Am. J. Phys. 27, 16 (1959); F. A. Berezin,Theor. Math. Phys. 6, 194 (1971); Dehai Bao and Z. Y. Zhu,Communic. Theor. Phys. 16, 201 (1991).
P. A. M. Dirac,The Principles of Quantum Mechanics, 4th eds. (Oxford University Press, Oxford, 1958).
See the remarks in Woodhouse's book,ibid., p. 162.
Dehai Bao and Z. Y. Zhu,J. Phys. A 25, 2381 (1992).
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Bao, D., Zhu, Z.Y. On Dirac's quantization condition. Found Phys Lett 8, 195–201 (1995). https://doi.org/10.1007/BF02187588
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DOI: https://doi.org/10.1007/BF02187588