3,219 research outputs found
Orthogonality criterion for banishing hydrino states from standard quantum mechanics
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
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
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
The blackbody radiation is analyzed in universes with 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
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
The intrinsically relativistic problem of spinless particles subject to a
general mixing of vector and scalar kink-like potentials () 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
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
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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