On a stationary Schrödinger equation with periodic magnetic potential
نویسندگان
چکیده
We prove existence results for a stationary Schr{\"o}dinger equation with periodic magnetic potential satisfying local integrability condition on the whole space using critical value function.
منابع مشابه
Wannier functions analysis of the nonlinear Schrödinger equation with a periodic potential.
In the present paper we use the Wannier function basis to construct lattice approximations of the nonlinear Schrödinger equation with a periodic potential. We show that the nonlinear Schrödinger equation with a periodic potential is equivalent to a vector lattice with long-range interactions. For the case-example of the cosine potential we study the validity of the so-called tight-binding appro...
متن کاملOn Non - Linear Schrödinger Equation with Magnetic Field
We study the non-linear Schödinger equation with time depending magnetic field without smallness assumption at infinity. We obtain some results on the Cauchy problem, WKB asymptotics and instability.
متن کاملPeriodic almost-Schrödinger equation for quasicrystals
A new method for finding electronic structure and wavefunctions of electrons in quasiperiodic potential is introduced. To obtain results it uses slightly modified Schrödinger equation in spaces of dimensionality higher than physical space. It enables to get exact results for quasicrystals without expensive non-exact calculations.
متن کاملSchrödinger 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 کاملModulational Instability for Nonlinear Schrödinger Equations with a Periodic Potential
We study the stability properties of periodic solutions to the Nonlinear Schrödinger (NLS) equation with a periodic potential. We exploit the symmetries of the problem, in particular the Hamiltonian structure and the U(1) symmetry. We develop a simple sufficient criterion that guarantees the existence of a modulational instability spectrum along the imaginary axis. In the case of small amplitud...
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: Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-matematicas
سال: 2021
ISSN: ['1578-7303', '1579-1505']
DOI: https://doi.org/10.1007/s13398-021-01011-9