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

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

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 ($\sim \mathrm{tanh} ,\gamma x$) 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

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