New solutions of the D-dimensional Klein-Gordon equation via mapping onto the nonrelativistic one-dimensional Morse potential

New exact analytical bound-state solutions of the D-dimensional Klein-Gordon equation for a large set of couplings and potential functions are obtained via mapping onto the nonrelativistic bound-state solutions of the one-dimensional generalized Morse potential. The eigenfunctions are expressed in terms of generalized Laguerre polynomials, and the eigenenergies are expressed in terms of solutions of irrational equations at the worst. Several analytical results found in the literature, including the so-called Klein-Gordon oscillator, are obtained as particular cases of this unified approac

How do incorrect results change the processing of arithmetic information? Evidence from a divided visual field experiment

Despite several recent important developments in understanding numerical processing of both isolated numbers and numbers in the context of arithmetic equations, the relative impact of congruency on high, compared to low, level processing remains unclear. The current study investigated hemispheric differences in the processing of arithmetic material, as a function of semantic and perceptual congruency, using a delayed answer verification task and divided visual field paradigm. A total of 37 participants (22 females and 15 males, mean age 30.06, SD 9.78) were presented unilaterally or bilaterally with equation results that were either correct or incorrect and had a consistent or inconsistent numerical notation. Statistical analyses showed no visual field differences in a notation consistency task, whereas when judgements had to be made on mathematical accuracy there was a right visual field advantage for incorrect equations that were notation consistent. These results reveal a clear differential processing of arithmetic information by the two cerebral hemispheres with a special emphasis on erroneous calculations. Faced with incorrect results and with a consistent numerical notation, the left hemisphere outperforms its right counterpart in making mathematical accuracy decisions

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