A Subtlety of the Schrödinger Picture Dynamics
نویسنده
چکیده
We address a mathematical and physical status of exotic (like e.g. fractal) solutions of the Schrödinger equation. To this end, we extend the formal meaning of the Schrödinger evolution of wave packets beyond the domain of the Hamiltonian. The dynamical importance of the finite mean energy condition is elucidated. PACS numbers: 03.65 Pb 1 Motivation For a simple Hamiltonian system whose energy operator Ĥ has a countably infinite spectrum {En} and normalized eigenvectors {|n〉}, so that Ĥ |n〉 = En|n〉 and 〈m|n〉 = δmn, any general pure state of the system is defined in terms of a normalized superposition |ψ, 0〉 . = ∑
منابع مشابه
Soliton Dynamics for Fractional Schrödinger Equations
We investigate the soliton dynamics for the fractional nonlinear Schrödinger equation by a suitable modulational inequality. In the semiclassical limit, the solution concentrates along a trajectory determined by a Newtonian equation depending of the fractional diffusion parameter.
متن کاملThe Schrödinger Wave Functional and S-branes
In this paper we will consider the minisuperspace approach to S-branes dynamics in the Schrödinger picture description. Time-evolution of vacuum wave functional for quantum field theory on S-brane is studied. Open string pair production is calculated. The analysis of density matrix for mixed states is also performed. On leave from Masaryk University, Brno
متن کاملExistence of Solutions for Non-necessarily Cooperative Systems Involving Schrödinger Operators
We study the existence of a solution for a non-necessarily cooperative system of n equations involving Schrödinger operators defined on RN and we study also a limit case (the Fredholm Alternative (FA)). We derive results for semilinear systems. 2000 Mathematics Subject Classification. 35J10, 35J45.
متن کاملDynamics on resonant clusters for the quintic non linear Schrödinger equation
— We construct solutions to the quintic nonlinear Schrödinger equation on the circle i∂tu+ ∂ 2 xu = ν |u| 4 u, ν ≪ 1, x ∈ S, t ∈ R, with initial conditions supported on arbitrarily many different resonant clusters. This is a sequel the work [5] of Benôıt Grébert and the second author.
متن کاملPerturbation Expansion and N -th Order Fermi Golden Rule of the Nonlinear Schrödinger Equations
In this paper we consider generalized nonlinear Schrödinger equations with external potentials. we compute the forth and the sixed order Fermi Golden Rules (FGR), conjectured in [GS2, GS3], which is used in a study of the asymptotic dynamics of trapped solitons.
متن کامل