The case of a single charged particle with potential energy is considered when the classical electromagnetic field is zero. The vector and scalar potentials describing this situation are not necessarily zero. When the conventional approach to radiation problems using the interaction A⋅p plus p⋅A plus A2 plus A0 (constants omitted) is used, time‐dependent probabilities are predicted if the vector potential A=−∇Λ≠0 even though the electromagnetic field is zero. The reason for this unphysical behavior is that eigenfunctions of the unperturbed Hamiltonian, which is not gauge invariant, are used to calculate the probability amplitudes. When a manifestly gauge‐invariant procedure is applied to this case the probabilities are constant in all gauges. The reason that physical results are obtained is that eigenstates of the energy operator are used to calculate the probability amplitudes.
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February 1983
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February 01 1983
Gauge invariance in quantum mechanics: zero electromagnetic field
Donald H. Kobe;
Donald H. Kobe
Department of Physics, North Texas State University, Denton, Texas 76203
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Kuo‐Ho Yang
Kuo‐Ho Yang
Theoretical Chemistry Institute, University of Wisconsin–Madison, Madison, Wisconsin 53706
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Am. J. Phys. 51, 163–168 (1983)
Article history
Received:
November 04 1981
Accepted:
March 08 1982
Citation
Donald H. Kobe, Kuo‐Ho Yang; Gauge invariance in quantum mechanics: zero electromagnetic field. Am. J. Phys. 1 February 1983; 51 (2): 163–168. https://doi.org/10.1119/1.13316
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