2,245 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
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
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
Relativistic quantum dynamics of scalar bosons under a full vector Coulomb interaction
The relativistic quantum dynamics of scalar bosons in the background of a
full vector coupling (minimal plus nonminimal vector couplings) is explored in
the context of the Duffin-Kemmer-Petiau formalism. The Coulomb phase shift is
determined for a general mixing of couplings and it is shown that the space
component of the nonminimal coupling is a {\it sine qua non} condition for the
exact closed-form scattering amplitude. It follows that the Rutherford cross
section vanishes in the absence of the time component of the minimal coupling.
Bound-state solutions obtained from the poles of the partial scattering
amplitude show that the time component of the minimal coupling plays an
essential role. The bound-state solutions depend on the nonminimal coupling and
the spectrum consists of particles or antiparticles depending on the sign of
the time component of the minimal coupling without chance for pair production
even in the presence of strong couplings. It is also shown that an accidental
degeneracy appears for a particular mixing of couplings.Comment: 8 pages, 1 table. arXiv admin note: text overlap with arXiv:1403.603
Orthogonality criterion for banishing hydrino states from standard quantum mechanics
Orthogonality criterion is used to show 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 Schrödinger, Klein-Gordon and Dirac equations.http://www.sciencedirect.com/science/article/B6TVM-4NNYJ65-7/1/042cc91461a3d63c306721d501970a5
- …