Abstract
We consider an oscillator subjected to a sudden change in equilibrium position or in effective spring constant, or both—to a “squeeze” in the language of quantum optics. We analyze the probability of transition from a given initial state to a final state, in its dependence on final-state quantum number. We make use of five sources of insight: Bohr-Sommerfeld quantization via bands in phase space, area of overlap between before-squeeze band and after-squeeze band, interference in phase space, Wigner function as quantum update of B-S band and near-zone Fresnel diffraction as mockup Wigner function.
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References
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Schleich, W., Walther, H. & Wheeler, J.A. Area in phase space as determiner of transition probability: Bohr-Sommerfeld bands, Wigner ripples, and Fresnel zones. Found Phys 18, 953–968 (1988). https://doi.org/10.1007/BF01909932
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DOI: https://doi.org/10.1007/BF01909932