Nonrelativistic quantum particles on the Minkowski plane

• URL: http://arxiv.org/abs/2002.11990v4
• Date: Sat, 23 May 2020 07:38:49 GMT
• Title: Nonrelativistic quantum particles on the Minkowski plane
• Authors: N. A. Gromov, I. V. Kostyakov, V. V. Kuratov
• Abstract summary: The quantum-mechanical problems of a nonrelativistic free particle, a harmonic oscillator and a Coulomb particle on Minkowski plane are discussed. The Schr"odinger equations for eigenvalues are obtained using the Beltrami-Laplas operator of the pseudo-Euclidean plane.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The quantum-mechanical problems of a nonrelativistic free particle, a harmonic oscillator and a Coulomb particle on Minkowski plane are discussed. The Schr\"odinger equations for eigenvalues are obtained using the Beltrami-Laplas operator of the pseudo-Euclidean plane and the corresponding potentials. It is shown that, in contrast to the standard problem on Euclidean plane, in addition to the continuous spectrum, a free particle has a discrete energy levels and a Coulomb particle, in addition to the discrete spectrum, has unstable states that describe the incidence of a particle on isotropic lines forming a metric cone.

Related papers

• A non-hermitean momentum operator for the particle in a box [49.1574468325115]
  We show how to construct the corresponding hermitean Hamiltonian for the infinite as well as concrete example. The resulting Hilbert space can be decomposed into a physical and unphysical subspace.
  arXiv  Detail & Related papers  (2024-03-20T12:51:58Z)
• Energy eigenstates of position-dependent mass particles in a spherical quantum dot [0.0]
  We obtain the exact energy spectrum of nonuniform mass particles for a collection of Hamiltonians in a three-dimensional approach to a quantum dot. The present results are of interest to atomic physics and quantum dot theory.
  arXiv  Detail & Related papers  (2023-11-23T21:34:43Z)
• Does a massless Goldstone boson exist? [0.0]
  The concept of a particle is analyzed within the frame-work of the theory of nonlinear quantum fields. Various states in which the field can exist for given parameters entering into the Lagrangian are considered.
  arXiv  Detail & Related papers  (2023-04-04T12:33:23Z)
• Canonical equivalence of a particle in a magnetic field to a simple oscillator [0.0]
  It is proved that a classical (respec. quantum) system consisting of a particle in a constant magnetic field is canonically (respec. unitarily) equivalent to a 2-dimensional harmonic oscillator plus a free particle.
  arXiv  Detail & Related papers  (2023-04-01T22:48:55Z)
• Intrinsic quantum dynamics of particles in brane gravity [0.0]
  We show that the stability of particle trajectories on the brane gives us the Bohr--Sommerfeld quantization condition. The particle's motion along the extra dimension allows us to formulate a geometrical version of the uncertainty principle. We show that the particle's motion along the extra dimension yields a quantized energy spectrum for bound states.
  arXiv  Detail & Related papers  (2023-03-20T13:41:07Z)
• Free particle trapped in an infinite quantum well examined through the discrete calculus model [0.0]
  We use the discrete approach to solve the Schr"odinger equations for a free particle and the quantum gas of free particles embedded in an infinite quantum well with the finite width. We obtain the expressions of energy eigenvalues, the eigenfunctions as well as the density matrix and partition function for the discrete case.
  arXiv  Detail & Related papers  (2023-03-14T20:10:18Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• Exact quantum-mechanical equations for particle beams [91.3755431537592]
  These equations present the exact generalizations of the well-known paraxial equations in optics. Some basic properties of exact wave eigenfunctions of particle beams have been determined.
  arXiv  Detail & Related papers  (2022-06-29T20:39:36Z)
• Fano Resonances in Quantum Transport with Vibrations [50.591267188664666]
  Quantum mechanical scattering continuum states coupled to a scatterer with a discrete spectrum gives rise to Fano resonances. We consider scatterers that possess internal vibrational degrees of freedom in addition to discrete states.
  arXiv  Detail & Related papers  (2021-08-07T12:13:59Z)
• Fano interference in quantum resonances from angle-resolved elastic scattering [62.997667081978825]
  We show that probing the angular dependence of the cross section allows us to unveil asymmetric Fano profiles in a single channel shape resonance. We observe a shift in the peak of the resonance profile in the elastic collisions between metastable helium and deuterium molecules.
  arXiv  Detail & Related papers  (2021-05-12T20:41:25Z)
• Quantum particle across Grushin singularity [77.34726150561087]
  We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
  arXiv  Detail & Related papers  (2020-11-27T12:53:23Z)

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.