Quantum Caustics for Systems with Quadratic Lagrangians
نویسندگان
چکیده
We study caustics in classical and quantum mechanics for systems with quadratic Lagrangians of the form L = 1 2 ẋ − 1 2 λ(t)x − μ(t)x. We derive a closed form of the transition amplitude on caustics and discuss their physical implications in the Gaussian slit (gedanken-)experiment. Application to the quantum mechanical rotor casts doubt on the validity of Jevicki’s correspondence hypothesis which states that in quantum mechanics, stationary points (instantons) arise as simple poles. PACS codes: 02.30.Hg; 03.65.-w; 03.65.Sq
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Quantum Caustics for Systems with Quadratic Lagrangians in Multi-Dimensions
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We study classical and quantum caustics for systems with quadratic Lagrangians of the form L = 1 2 ẋ − 1 2 λ(t)x − μ(t)x. After deriving the transition amplitude on caustics in a closed form, we consider the Gaussian slit experiment and point out that the focusing around caustics is stabilized against initial momentum fluctuations by quantum effect. PACS codes: 02.30.Hg; 03.65.-w; 03.65.Sq
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