3,219 research outputs found

    Orthogonality criterion for banishing hydrino states from standard quantum mechanics

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    Orthogonality criterion is used to shown in a very simple and general way that anomalous bound-state solutions for the Coulomb potential (hydrino states) do not exist as bona fide solutions of the Schr\"{o}dinger, Klein-Gordon and Dirac equations.Comment: 6 page

    Effects of a mixed vector-scalar screened Coulomb potential for spinless particles

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    The problem of a spinless particle subject to a general mixing of vector and scalar screened Coulomb potentials in a two-dimensional world is analyzed and its bounded solutions are found. Some unusual results, including the existence of a bona fide solitary zero-eigenmode solution, are revealed for the Klein-Gordon equation. The cases of pure vector and scalar potentials, already analyzed in previous works, are obtained as particular cases.Comment: 13 pages, 2 figure

    Quasi-exactly-solvable confining solutions for spin-1 and spin-0 bosons in (1+1)-dimensions with a scalar linear potential

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    We point out a misleading treatment in the recent literature regarding confining solutions for a scalar potential in the context of the Duffin-Kemmer-Petiau theory. We further present the proper bound-state solutions in terms of the generalized Laguerre polynomials and show that the eigenvalues and eigenfunctions depend on the solutions of algebraic equations involving the potential parameter and the quantum number.Comment: 8 pages, 1 figur

    The Blackbody Radiation in D-Dimensional Universes

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    The blackbody radiation is analyzed in universes with DD spatial dimensions. With the classical electrodynamics suited to the universe in focus and recurring to the hyperspherical coordinates, it is shown that the spectral energy density as well as the total energy density are sensible to the dimensionality of the universe. Wien's displacement law and the Stefan-Boltzmann law are properly generalized

    Confinement of neutral fermions by a pseudoscalar double-step potential in (1+1) dimensions

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    The problem of confinement of neutral fermions in two-dimensional space-time is approached with a pseudoscalar double-step potential in the Dirac equation. Bound-state solutions are obtained when the coupling is of sufficient intensity. The confinement is made plausible by arguments based on effective mass and anomalous magnetic interaction.Comment: 8 pages, 1 figur

    Effects of a mixed vector-scalar kink-like potential for spinless particles in two-dimensional spacetime

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    The intrinsically relativistic problem of spinless particles subject to a general mixing of vector and scalar kink-like potentials (tanh,γx\sim \mathrm{tanh} ,\gamma x) is investigated. The problem is mapped into the exactly solvable Surm-Liouville problem with the Rosen-Morse potential and exact bounded solutions for particles and antiparticles are found. The behaviour of the spectrum is discussed in some detail. An apparent paradox concerning the uncertainty principle is solved by recurring to the concept of effective Compton wavelength.Comment: 13 pages, 4 figure

    A Laplace transform approach to the quantum harmonic oscillator

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    The one-dimensional quantum harmonic oscillator problem is examined via the Laplace transform method. The stationary states are determined by requiring definite parity and good behaviour of the eigenfunction at the origin and at infinity

    Revisiting the quantum harmonic oscillator via unilateral Fourier transforms

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    The literature on the exponential Fourier approach to the one-dimensional quantum harmonic oscillator problem is revised and criticized. It is shown that the solution of this problem has been built on faulty premises. The problem is revisited via the Fourier sine and cosine transform method and the stationary states are properly determined by requiring definite parity and square-integrable eigenfunctions.Comment: 11 page
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