Fractional Schrödinger equation.
نویسنده
چکیده
Some properties of the fractional Schrödinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schrödinger equation we find the energy spectra of a hydrogenlike atom (fractional "Bohr atom") and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schrödinger equations.
منابع مشابه
Fractional Schrödinger dynamics and decoherence
Abstract. We study the dynamics of the Schrödinger equation with a fractional Laplacian (−∆), and the decoherence of the solution is observed in certain cases. Analytically, we find equations describing the dynamics of the expected position and expected momentum in the fractional Schödinger equation, equations that are the fractional counterpart of the Newtonian equations of motion for the non-...
متن کاملFractional Schrödinger equation in optics.
In quantum mechanics, the space-fractional Schrödinger equation provides a natural extension of the standard Schrödinger equation when the Brownian trajectories in Feynman path integrals are replaced by Levy flights. Here an optical realization of the fractional Schrödinger equation, based on transverse light dynamics in aspherical optical cavities, is proposed. As an example, a laser implement...
متن کاملFractional Ginzburg–Landau equation for fractal media
We derive the fractional generalization of the Ginzburg–Landau equation from the variational Euler–Lagrange equation for fractal media. To describe fractal media we use the fractional integrals considered as approximations of integrals on fractals. Some simple solutions of the Ginzburg–Landau equation for fractal media are considered and different forms of the fractional Ginzburg–Landau equatio...
متن کاملGround States for the Fractional Schrödinger Equation
In this article, we show the existence of ground state solutions for the nonlinear Schrödinger equation with fractional Laplacian (−∆)u+ V (x)u = λ|u|u in R for α ∈ (0, 1). We use the concentration compactness principle in fractional Sobolev spaces Hα for α ∈ (0, 1). Our results generalize the corresponding results in the case α = 1.
متن کاملEffective Potential from the Generalized Time-Dependent Schrödinger Equation
We analyze the generalized time-dependent Schrödinger equation for the force free case, as a generalization, for example, of the standard time-dependent Schrödinger equation, time fractional Schrödinger equation, distributed order time fractional Schrödinger equation, and tempered in time Schrödinger equation. We relate it to the corresponding standard Schrödinger equation with effective potent...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Physical review. E, Statistical, nonlinear, and soft matter physics
دوره 66 5 Pt 2 شماره
صفحات -
تاریخ انتشار 2002