相关论文: On separable Schr\"odinger equations

We classify (1+3)-dimensional Pauli equations for a spin-1/2 particle interacting with the electro-magnetic field, that are solvable by the method of separation of variables. As a result, we obtain the eleven classes of vector-potentials of…

We suggest an effective approach to separation of variables in the Schr\"odinger equation with two space variables. Using it we classify inequivalent potentials $V(x_1,x_2)$ such that the corresponding Schr\" odinger equations admit…

With a number of special Hamiltonians, solutions of the Schr\"{o}dinger equation may be found by separation of variables in more than one coordinate system. The class of potentials involved includes a number of important examples, including…

We consider a two-dimensional integrable Hamiltonian system with a vector and scalar potential in quantum mechanics. Contrary to the case of a pure scalar potential, the existence of a second order integral of motion does not guarantee the…

By constructing the commutative operators chain, we derive the integrable conditions for solving the eigenfunctions of Dirac equation and Schr\"odinger equation. These commutative relations correspond to the intrinsic symmetry of the…

The Schr\"odinger equation for a charged particle in the field of a nonrelativistic electric quadrupole in two dimensions is known to be separable in spherical coordinates. We investigate the occurrence of bound states of negative energy…

Using cylindrical coordinates, we consider position-dependent mass (PDM) charged particles moving under the influence of magnetic, Aharonov-Bohm flux, and a pseudoharmonic or a generalized Killingbeck-type potential fields. We implement the…

The Schr\"odinger equation in the presence of an external electromagnetic field is an important problem in computational quantum mechanics. It also provides a nice example of a differential equation whose flow can be split with benefit into…

All equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces, provided that Hamilton-Jacobi equation and Klein-Gordon-Fock equation for a charged test particle can be integrated by the method of complete…

We consider d-dimensional time dependent Schr\"odinger equations on the Hilbert space of square integrable functions. We assume magnetic and scalar potentials are almost critically singular with respect to spatial variables both locally and…

Exact analytic solutions to the Schr\"odinger equation for an electron moving in three dimensional potentials have been studied. These solutions can correspond to metals, semiconductors, or insulators. We show that there is an efficient…

Found all equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces, provided that the equations of motion of the classical charged test particles are integrated by the method of complete separation of…

We consider the inverse coefficient problem of simultaneously determining the space dependent electromagnetic potential, the zero-th order coupling term and the first order coupling vector of a two-state Schr\"odinger equation in a bounded…

The Schr\"odinger theory of electrons in an external electromagnetic field can be described from the perspective of the individual electron via the `Quantal Newtonian' laws (or differential virial theorems). These laws are in terms of…

We study $(2+1)$ dimensional Dirac equation with complex scalar and Lorentz scalar potentials. It is shown that the Dirac equation admits exact analytical solutions with real eigenvalues for certain complex potentials while for another…

We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is…

We investigate existence and qualitative behaviour of solutions to nonlinear Schr\"odinger equations with critical exponent and singular electromagnetic potentials. We are concerned with magnetic vector potentials which are homogeneous of…

Multi-time wave functions are wave functions that have a time variable for every particle, such as $\phi(t_1,x_1,\ldots,t_N,x_N)$. They arise as a relativistic analog of the wave functions of quantum mechanics but can be applied also in…

We found that the two-dimensional Schr\"odinger equation for 3 electrons in an homogeneous magnetic field (perpendicular to the plane) and a parabolic scalar confinement potential (frequency $\omega_0$) has exact analytical solutions in the…

We consider the semilinear electromagnetic Schr\"{o}dinger equation (-i\nabla+A(x))^{2}u + V(x)u = |u|^{2^{\ast}-2}u, u\in D_{A,0}^{1,2}(\Omega,\mathbb{C}), where $\Omega=(\mathbb{R}^{m}\smallsetminus{0})\times\mathbb{R}^{N-m}$ with $2\leq…