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PRODID:-//Nonequilibrium quantum and statistical physics - ECPv4.6.21//NONSGML v1.0//EN
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X-WR-CALNAME:Nonequilibrium quantum and statistical physics
X-ORIGINAL-URL:https://chaos.fmf.uni-lj.si
X-WR-CALDESC:Events for Nonequilibrium quantum and statistical physics
BEGIN:VEVENT
DTSTART;TZID=Europe/Ljubljana:20171128T160000
DTEND;TZID=Europe/Ljubljana:20171128T180000
DTSTAMP:20180817T205539
CREATED:20171121T103051Z
LAST-MODIFIED:20171209T102939Z
UID:532-1511884800-1511892000@chaos.fmf.uni-lj.si
SUMMARY:Marko Robnik: Application of the WKB method in 1D linear and nonlinear time-dependent oscillators
DESCRIPTION:The WKB method is an important analytic tool for solving numerous problems in\nmathematical physics of 1D systems\, for example the stationary (time-independent)\nSchrödinger equation in one dimension\, or the classical dynamics of one-dimensional\ntime-dependent (nonautonomous) Hamilton oscillators. I shall review the standard\nWKB method including the exact explicit solutions to all orders\, published by Rob-\nnik and Romanovski (2000)\, and applied in a series of papers. Among other results\nwe have shown that the application of the method in cases of the Schrödinger equa-\ntion with exactly solvable potentials leads to an infinite series to all orders\, that the\nseries converges and the sum reproduces the known exact eigenenergies. We shall\nlook in particular at the case of the time-dependent one-dimensional linear Hamilto-\nnian oscillator\, and then I shall present the approach towards generalizing the WKB\nmethod for the case of one-dimensional time-dependent nonlinear Hamiltonian oscil-\nlators having quadratic kinetic energy and homogeneous power law potential\, which\nincludes e.g. the quartic oscillator\, and of course also the linear oscillator. I will\nshow that the nonlinear method\, although only in the leading approximation\, is very\nuseful and accurate. We also shall touch upon possible generalizations. \n* Marko Robnik\, CAMTP\, Univerza v Mariboru \n
URL:https://chaos.fmf.uni-lj.si/?tribe_events=marko-robnik-application-of-the-wkb-method-in-1d-linear-and-nonlinear-time-dependent-oscillators
LOCATION:Jadranska 19\, Ljubljana\, Slovenia
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