相关论文: Nonrelativistic Green's function for systems with …

The extension of strongly anisotropic or dynamical scaling to local scale invariance is investigated. For the special case of an anisotropy or dynamical exponent $\theta=z=2$, the group of local scale transformation considered is the…

In a recent paper by Jafarov, Nagiyev, Oste and Van der Jeugt (2020 {\sl J.\ Phys.\ A} {\bf 53} 485301), a confined model of the non-relativistic quantum harmonic oscillator, where the effective mass and the angular frequency are dependent…

In this paper, we study the existence of positive solutions for nonlinear fractional differential equations with a singular weight. We derive Green's function and corresponding integral operator and then examine the compactness of the…

The modulational instability in the class of NLS equations is discussed using a statistical approach. A kinetic equation for the two-point correlation function is studied in a linear approximation, and an integral stability equation is…

We propose homogeneous metrics of Petrov type III that describe gyrating Schrodinger geometries as duals to some non-relativistic field theories, in which the Schrodinger symmetry is broken further so that the phase space has a linear…

We construct the Hadamard Green's function by using the eigenfunction, which are obtained by solving the wave equation for the massless conformal scalar field on the S^n-1 of a n-dimensional closed, static universe. We also consider the…

It is proposed that the Schrodinger equation for a free point particle has non-linear corrections which depend on the mass of the particle. It is assumed that the corrections become extremely small when the mass is much smaller or much…

In this paper, we present a variational treatment of the linear dependence for a non-orthogonal time-dependent basis set in solving the Schr\"odinger equation. The method is based on: i) the definition of a linearly independent working…

It is shown that the Green's function on a finite lattice in arbitrary space dimension can be obtained from that of an infinite lattice by means of translation operator. Explicit examples are given for one- and two-dimensional lattices.

Nonperturbative dynamic theory has a particular advantage in studying the transport in a quantum impurity system in a steady state. Here, we develop a new approach for obtaining the retarded Green's function expressed in resolvent form. We…

We prove the existence and pointwise bounds of the Green functions for stationary Stokes systems with measurable coefficients in two dimensional domains. We also establish pointwise bounds of the derivatives of the Green functions under a…

The non-equilibrium Green's function formalism for infinitely extended reservoirs coupled to a finite system can be derived by solving the equations of motion for a tight-binding Hamiltonian. While this approach gives the correct density…

We construct the Green function for second-order elliptic equations in non-divergence form when the mean oscillations of the coefficients satisfy the Dini condition. We show that the Green's function is BMO in the domain and establish…

The study of the Schr\"{o}dinger equation with the position-dependent effective mass has attracted a lot of attention, due to its applications in many fields of physics, including the properties of the semiconductors, semiconductor…

Exact analytical, closed-form solutions, expressed in terms of special functions, are presented for the case of a three-dimensional nonlinear quantum oscillator with a position dependent mass. This system is the generalization of the…

We discuss the relationship between exact solvability of the Schroedinger equation, due to a spatially dependent mass, and the ordering ambiguity. Some examples show that, even in this case, one can find exact solutions. Furthermore, it is…

We investigate the Schrodinger equation for a particle with a nonuniform solitonic mass density. First, we discuss in extent the (nontrivial) position-dependent mass $V(x)=0$ case whose solutions are hypergeometric functions in…

We obtain exact moving and stationary, spatially periodic and localized solutions of a generalized discrete nonlinear Schr\"odinger equation. More specifically, we find two different moving periodic wave solutions and a localized moving…

New exactly solvable quantum models are obtained with the help of the supersymmetric extencion of the nonstationary Schr/"odinger equation.

We employ the point canonical transformation (PCT) to solve the D-dimensional Schr\"{o}dinger equation with position-dependent effective mass (PDEM) function for two molecular pseudoharmonic and modified Kratzer (Mie-type) potentials. In…