General pseudo self-adjoint boundary conditions for a 1D KFG particle in a box

• URL: http://arxiv.org/abs/2301.01565v3
• Date: Mon, 20 Mar 2023 13:04:43 GMT
• Title: General pseudo self-adjoint boundary conditions for a 1D KFG particle in a box
• Authors: Salvatore De Vincenzo
• Abstract summary: We consider a 1D Klein-Fock-Gordon particle in a finite interval, or box. We write the most general set of pseudo self-adjoint boundary conditions for the Hamiltonian operator.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider a 1D Klein-Fock-Gordon particle in a finite interval, or box. We construct for the first time the most general set of pseudo self-adjoint boundary conditions for the Hamiltonian operator that is present in the first order in time 1D Klein-Fock-Gordon wave equation, or the 1D Feshbach-Villars wave equation. We show that this set depends on four real parameters and can be written in terms of the one-component wavefunction for the second order in time 1D Klein-Fock-Gordon wave equation and its spatial derivative, both evaluated at the endpoints of the box. Certainly, we write the general set of pseudo self-adjoint boundary conditions also in terms of the two-component wavefunction for the 1D Feshbach-Villars wave equation and its spatial derivative, evaluated at the ends of the box; however, the set actually depends on these two column vectors each multiplied by the singular matrix that is present in the kinetic energy term of the Hamiltonian. As a consequence, we found that the two-component wavefunction for the 1D Feshbach-Villars equation and its spatial derivative do not necessarily satisfy the same boundary condition that these quantities satisfy when multiplied by the singular matrix. In any case, given a particular boundary condition for the one-component wavefunction of the standard 1D Klein-Fock-Gordon equation and using the pair of relations that arise from the very definition of the two-component wavefunction for the 1D Feshbach-Villars equation, the respective boundary condition for the latter wavefunction and its derivative can be obtained. Our results can be extended to the problem of a 1D Klein-Fock-Gordon particle moving on a real line with a point interaction (or a hole) at one point.

Related papers

• Characterizing Klein-Fock-Gordon-Majorana particles in (1+1) dimensions [0.0]
  We write first-order equations in the time derivative that do not have a Hamiltonian form. We examine the nonrelativistic limit of one of the first-order 1D Majorana equations.
  arXiv  Detail & Related papers  (2023-12-18T06:54:56Z)
• Double-scale theory [77.34726150561087]
  We present a new interpretation of quantum mechanics, called the double-scale theory. It is based on the simultaneous existence of two wave functions in the laboratory reference frame. The external wave function corresponds to a field that pilots the center-of-mass of the quantum system. The internal wave function corresponds to the interpretation proposed by Edwin Schr"odinger.
  arXiv  Detail & Related papers  (2023-05-29T14:28:31Z)
• In-Gap Band Formation in a Periodically Driven Charge Density Wave Insulator [68.8204255655161]
  Periodically driven quantum many-body systems host unconventional behavior not realized at equilibrium. We investigate such a setup for strongly interacting spinless fermions on a chain, which at zero temperature and strong interactions form a charge density wave insulator.
  arXiv  Detail & Related papers  (2022-05-19T13:28:47Z)
• Zero-range potentials for Dirac particles: Bound-state problems [0.0]
  A Dirac particle in $mathbbR3$ is bound by $Ngeqslant1$ spatially distributed zero-range potentials. Wave functions may be normalized so that their self-pseudo-products are plus one, minus one or zero.
  arXiv  Detail & Related papers  (2022-03-18T11:59:56Z)
• Regularized Zero-Range Hamiltonian for a Bose Gas with an Impurity [77.34726150561087]
  We study the Hamiltonian for a system of N identical bosons interacting with an impurity. We introduce a three-body force acting at short distances. The effect of this force is to reduce to zero the strength of the zero-range interaction between two particles.
  arXiv  Detail & Related papers  (2022-02-25T15:34:06Z)
• Wave functions for high-symmetry, thin microstrip antennas and two-dimensional quantum boxes [48.7576911714538]
  For a spinless quantum particle in a one-dimensional box or an electromagnetic wave in a one-dimensional cavity, the respective Dirichlet and Neumann boundary conditions both lead to non-degenerate wave functions. In two spatial dimensions, the symmetry of the box or microstrip antenna is an important feature that has often been overlooked in the literature.
  arXiv  Detail & Related papers  (2021-08-18T00:57:42Z)
• On the boundary conditions for the 1D Weyl-Majorana particle in a box [0.0]
  In (1+1) space-time dimensions, we have two particles that are Weyl and Majorana particles at the same time---1D Weyl-Majorana particles. We investigate and discuss this issue and demonstrate that for a 1D Weyl-Majorana particle in a box, the nonzero components, and therefore the chiral wave functions, only admit the periodic and antiperiodic boundary conditions.
  arXiv  Detail & Related papers  (2020-11-08T16:03:15Z)
• Noninteracting Electrons in a Prototypical One-Dimensional Sinusoidal Potential [0.0]
  A prototypical model of a one-dimensional metallic monatomic solid containing noninteracting electrons is studied. The time-independent Schrodinger equation can be written in reduced variables as a Mathieu equation for which numerically-exact solutions for the band structure and wave functions are obtained.
  arXiv  Detail & Related papers  (2020-03-14T14:41:34Z)
• Radiative topological biphoton states in modulated qubit arrays [105.54048699217668]
  We study topological properties of bound pairs of photons in spatially-modulated qubit arrays coupled to a waveguide. For open boundary condition, we find exotic topological bound-pair edge states with radiative losses. By joining two structures with different spatial modulations, we find long-lived interface states which may have applications in storage and quantum information processing.
  arXiv  Detail & Related papers  (2020-02-24T04:44:12Z)
• External and internal wave functions: de Broglie's double-solution theory? [77.34726150561087]
  We propose an interpretative framework for quantum mechanics corresponding to the specifications of Louis de Broglie's double-solution theory. The principle is to decompose the evolution of a quantum system into two wave functions. For Schr"odinger, the particles are extended and the square of the module of the (internal) wave function of an electron corresponds to the density of its charge in space.
  arXiv  Detail & Related papers  (2020-01-13T13:41:24Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.