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The exact transition probabilities of quantum-mechanical oscillators calculated by the phase-space method

Published online by Cambridge University Press:  24 October 2008

M. S. Bartlett  and
J. E. Moyal
M. S. Bartlett
Affiliation:
Department of MathematicsUniversity of Manchester
J. E. Moyal
Affiliation:
Department of MathematicsUniversity of Manchester
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Extract

The ‘phase-space’ method in quantum theory is used to derive exact expressions for the transition probabilities of a perturbed oscillator. Comparison with the approximate results obtained by perturbation methods shows that the latter must be multiplied by an exponential factor exp (− ∊/ℏω), where ∊ is the non-fluctuating part of the work done by the perturbing forces; as long as ∊ is small, exp (− ∊/ℏω) ˜ 1 and only dipole transitions have an appreciable probability. As the perturbation energy increases, however, this is no longer true, and multipole transitions become progressively more probable, the most probable ones being those for which the change in energy is approximately equal to the work done by the perturbing forces.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 45 , Issue 4 , October 1949 , pp. 545 - 553
Copyright
Copyright © Cambridge Philosophical Society 1949

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References

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