Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Gazzetta chimica italiana

Conventional vs gauge invariant quantum transition probabilities in simple systems

Giovanni P. Arrighini, Carla Guidotti, Nicola Durante

Published Jan 1, 1988• 0 citations
OpenAlex

Related papers

Conventionalvs. Gauge-invariant quantum transition probabilities in simple systems. Morse oscillator

Giovanni P. Arrighini, Carla Guidotti, N. Durante

Il Nuovo Cimento D•Oct 1, 1987•2 citations

On the gauge invariance of transition probabilities

Saul T. Epstein

Chemical Physics Letters•Sep 1, 1979•6 citations

Gauge-invariant time-dependent perturbation theory. II. degenerate case

Kuo‐Ho Yang

For pt.I see ibid., vol.15, p.1201 (1982). The author formulates a manifestly gauge-invariant time-dependent perturbation theory for a nonrelativistic spinless charged particle interacting with a classical external electromagnetic radiation field. The treatment of the degenerate bound states and the states in the continuum is considered. It is found that the gauge-invariant and the conventional perturbative solutions agree on the net transition rates but disagree on the transition amplitudes and transition probabilities. The treatment of a realistic physical system can be obtained by combining the treatment here with that for a nondegenerate system.

Journal of Physics A Mathematical and General•Apr 1, 1983•11 citations

The question of gauge dependence of transition probabilities in quantum mechanics: Facts, myths and misunderstandings

Yakir Aharonov, C. K. Au

Physics Letters A•Nov 1, 1981•32 citations

Gauge invariant formulation of the interaction of electromagnetic radiation and matter

Donald H. Kobe, Arthur L. Smirl

The conventional perturbation theory in quantum mechanics for the interaction of electromagnetic radiation with matter, which is based on the time-dependent vector and scalar potentials, is shown to be dependent on the gauge. The problem is reformulated, using the approach of Yang, in a gauge-invariant way, in which the transitions between states are induced by the quantum-mechanical power operator. In order to use an unperturbed Hamiltonian which does not involve the electromagnetic field, the gauge is chosen to give the electric dipole interaction. This choice can be made if the magnetic field is negligible and the electric field is slowly varying over atomic dimensions. For a comparison of the gauge-invariant and conventional formulation, a two-level atom in a radiation field is considered. For the probability that an atom originally in the lower state will make a transition to the upper state when the field is not in resonance, the gauge-invariant formulation gives the correct result, whereas the gauge-dependent formulation gives an incorrect result.

American Journal of Physics•Jun 1, 1978•118 citations

Could Inelastic Interactions Induce Quantum Probabilistic Transitions?

Shan Gao

Cambridge University Press eBooks•Apr 20, 2018•4 citations
For pt.I see ibid., vol.15, p.1201 (1982). The author formulates a manifestly gauge-invariant time-dependent perturbation theory for a nonrelativistic spinless charged particle interacting with a classical external electromagnetic radiation field. The treatment of the degenerate bound states and the states in the continuum is considered. It is found that the gauge-invariant and the conventional perturbative solutions agree on the net transition rates but disagree on the transition amplitudes and transition probabilities. The treatment of a realistic physical system can be obtained by combining the treatment here with that for a nondegenerate system.
The conventional perturbation theory in quantum mechanics for the interaction of electromagnetic radiation with matter, which is based on the time-dependent vector and scalar potentials, is shown to be dependent on the gauge. The problem is reformulated, using the approach of Yang, in a gauge-invariant way, in which the transitions between states are induced by the quantum-mechanical power operator. In order to use an unperturbed Hamiltonian which does not involve the electromagnetic field, the gauge is chosen to give the electric dipole interaction. This choice can be made if the magnetic field is negligible and the electric field is slowly varying over atomic dimensions. For a comparison of the gauge-invariant and conventional formulation, a two-level atom in a radiation field is considered. For the probability that an atom originally in the lower state will make a transition to the upper state when the field is not in resonance, the gauge-invariant formulation gives the correct result, whereas the gauge-dependent formulation gives an incorrect result.