On Singular Potential of the Schrödinger Equation
نویسندگان
چکیده
منابع مشابه
Schrödinger equation of general potential
It is well known that the Schrödinger equation is only suitable for the particle in common potential V (~r, t). In this paper, a general Quantum Mechanics is proposed, where the Lagrangian is the general form. The new quantum wave equation can describe the particle which is in general potential V (~r, ~̇r, t). We think these new quantum wave equations can be applied in many fields. PACS numbers:...
متن کاملSingular Solutions of the Biharmonic Nonlinear Schrödinger Equation
We consider singular solutions of the L 2-critical biharmonic nonlinear Schrödinger equation. We prove that the blowup rate is bounded by a quartic-root, the solution approaches a quasi–self-similar profile, and a finite amount of L 2-norm, which is no less than the critical power, concentrates into the singularity. We also prove the existence of a ground-state solution. We use asymptotic analy...
متن کاملFourth order real space solver for the time-dependent Schrödinger equation with singular Coulomb potential
We present a novel numerical method and algorithm for the solution of the 3D axially symmetric timedependent Schrödinger equation in cylindrical coordinates, involving singular Coulomb potential terms besides a smooth time-dependent potential. We use fourth order finite difference real space discretization, with special formulae for the arising Neumann and Robin boundary conditions along the sy...
متن کاملṕ Estimates for the Schrödinger Equation on the Line and Inverse Scattering for the Nonlinear Schrödinger Equation with a Potential ∗
In this paper I prove a L − L estimate for the solutions of the one–dimensional Schrödinger equation with a potential in Lγ where in the generic case γ > 3/2 and in the exceptional case (i.e. when there is a half–bound state of zero energy) γ > 5/2. I use this estimate to construct the scattering operator for the nonlinear Schrödinger equation with a potential. I prove moreover, that the low–en...
متن کاملThe Nonlinear Schrödinger Equation with a Strongly Anisotropic Harmonic Potential
The nonlinear Schrödinger equation with general nonlinearity of polynomial growth and harmonic confining potential is considered. More precisely, the confining potential is strongly anisotropic; i.e., the trap frequencies in different directions are of different orders of magnitude. The limit as the ratio of trap frequencies tends to zero is carried out. A concentration of mass on the ground st...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Modern Physics Letters A
سال: 2003
ISSN: 0217-7323,1793-6632
DOI: 10.1142/s0217732303011885