0 Quantum Integrals of Motion for Variable Quadratic
نویسنده
چکیده
We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schrödinger equation with variable quadratic Hamiltonians. An extension of the Lewis–Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application.
منابع مشابه
4 Quadratic integrals of motion for the systems of identical particles - quantum case
The quantum dynamical systems of identical particles admitting an additional integral quadratic in momenta are considered. It is found that an appropriate ordering procedure exists which allows to convert the classical integrals into their quantum counterparts. The relation to the separation of variables in Schroedinger equation is discussed. supported by KBN grant 5 P03B06021 supported by KBN ...
متن کاملQuadratic integrals of motion for the systems of identical particles - quantum case
The quantum dynamical systems of identical particles admitting an additional integral quadratic in momenta are considered. It is found that an appropriate ordering procedure exists which allows to convert the classical integrals into their quantum counterparts. The relation to the separation of variables in Schroedinger equation is discussed. supported by KBN grant 5 P03B06021 supported by KBN ...
متن کاملCentral limit theorems for multiple Skorohod integrals
In this paper, we prove a central limit theorem for a sequence of multiple Skorohod integrals using the techniques of Malliavin calculus. The convergence is stable, and the limit is a conditionally Gaussian random variable. Some applications to sequences of multiple stochastic integrals, and renormalized weighted quadratic variation of the fractional Brownian motion are discussed.
متن کامل0 p - ADIC PATH INTEGRALS FOR QUADRATIC ACTIONS
The Feynman path integral in p-adic quantum mechanics is considered. The probability amplitude K p (x ′′ , t ′′ ; x ′ , t ′) for one-dimensional systems with quadratic actions is calculated in an exact form, which is the same as that in ordinary quantum mechanics.
متن کاملFactorization of the constants of the motion
A complete set of first integrals, or constants of the motion, for a model system is constructed using “factorization”, as described below. The system is described by the effective Feynman Lagrangian L = 14 [mẍ(t) + 2mλẋ(t) + ∂xV (x(t))] , with one of the simplest, non-trivial, potentials V (x) = 12mω x selected for study. Four new, explicitly time-dependent, constants of the motion ci±, i = 1,...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010