相关论文: Variational methods in relativistic quantum mechan…
We investigate the quantum motion of a neutral Dirac particle bouncing on a mirror in curved spacetime. We consider different geometries: Rindler, Kasner-Taub and Schwarzschild, and show how to solve the Dirac equation by using geometrical…
In this work, a spin $\frac 12$ relativistic particle described by a generalized potential containing both the Coulomb potential and a Lorentz scalar potential in Dirac equation is investigated in terms of the generalized ladder operators…
Seeking for a relativistic generalisation of the non-relativistic Schroedinger equation, one very soon arrives at equations with a square-root operator by having applied the quantum mechanical correspondence principle to the formula of…
We consider the quantum simulation of relativistic quantum mechanics, as described by the Dirac equation and classical potentials, in trapped-ion systems. We concentrate on three problems of growing complexity. First, we study the…
We discuss how to generalize a Dirac operator such that the solution of a Dirac equation is of bounded variation rather than continuous. We build the spectral theory for generalized Dirac operators and discuss the connection between them…
In this work it is studied a quasilinear elliptic problem in the whole space $\mathbb{R}^N$ involving the $1-$Laplacian operator, with potentials which can vanish at infinity. The Euler-Lagrange functional is defined in a space whose…
The quantum mechanical motion of a relativistic particle in a non-continuous spacetime is investigated. The spacetime model is a dense, rationale subset of two-dimensional Minkowski spacetime. Solutions of the Dirac equation are calculated…
We apply the extended Nikiforov-Uvarov method to the non-relativistic limit of the Dirac equation with a Coulomb potential in spaces of constant curvature. In this case, the radial equation reduces to the Heun equation, and the extended…
In the variational framework, we study the electronic energy spectrum of massless Dirac fermions of graphene subjected to one-dimensional oscillating magnetic and electrostatic fields centered around a constant uniform static magnetic…
The Dirac equation plays an essential role in the relativistic quantum systems, which is reduced to a form similar to Schrodinger equation when a certain potential's type is selected as the Cornell potential. By choosing the generalized…
We first study the linear eigenvalue problem for a planar Dirac system in the open half-line and describe the nodal properties of its solution by means of the rotation number. We then give a global bifurcation result for a planar nonlinear…
Exact solutions of the Dirac equation in external electromagnetic background fields are very helpful for understanding non-perturbative phenomena in quantum electrodynamics (QED). However, for the limited set of known solutions, the field…
In the present article, using a further generalization of the algebraic method of separation of variables, the Dirac equation is separated in a family of space-times where it is not possible to find a complete set of first order commuting…
Any given system of ordinary differential equations in $n$-dimensional configuration space can be obtained from a peculiar variational problem with one local symmetry. The obtained action functional leads to the Hamiltonian formulation in…
A general dynamical invariant operator for three coupled time-dependent oscillators is derived. Although the obtained invariant operator satisfies the Liouville-von Neumann equation, its mathematical formula is somewhat complicated due to…
We develop in this paper a new framework for discrete calculus of variations when the actions have densities involving an arbitrary discretization operator. We deduce the discrete Euler-Lagrange equations for piecewise continuous critical…
This article deals with the existence and non-existence of positive solutions for the eigenvalue problem driven by nonhomogeneous fractional $p\& q$ Laplacian operator with indefinite weights $$\left(-\Delta_p\right)^{\alpha}u +…
The ambiguity involved in the definition of effective-mass Hamiltonians for nonrelativistic models is resolved using the Dirac equation. The multistep approximation is extended for relativistic cases allowing the treatment of arbitrary…
Dirac operators on curved space-times are introduced with the help of a new point-view that observers have to be included in the formulation of natural laws. The class of Dirac operators are Lorentz invariant in the sense that the…
I argue that the linearity of quantum mechanics is an emergent feature at the Planck scale, along with the manifold structure of space-time. In this regime the usual causality violation objections to nonlinearity do not apply, and nonlinear…