Quantum dynamics of relativistic bosons through nonminimal vector square potentials

Abstract

The dynamics of relativistic bosons (scalar and vectorial) through nonminimal vector square (well and barrier) potentials is studied in the Duffin-Kemmer-Petiau (DKP) formalism. We show that the problem can be mapped in effective Schrödinger equations for a component of the DKP spinor. An oscillatory transmission coefficient is found and there is total reflection. Additionally, the energy spectrum of bound states is obtained and reveals the Schiff-Snyder-Weinberg effect, for specific conditions the potential lodges bound states of particles and antiparticles.

A note on the Duffin-Kemmer-Petiau equation in (1+1) space-time dimensions

“…We illustrate this equivalence by explicitly building the lowest dimensional (irreducible) representation of the theory. At the end we comment how our result explain why several authors in recent years found identical results for both the spin-0 and spin-1 sectors of the (3+1) dimensional DKP equation when the dynamics is restricted to only one space dimension [10][11][12][13][14][15][16][17][18][19][20] .…”

“…Our result is also useful to explain why in several recent papers the authors obtained the same results for both the spin-0 and spin-1 sectors of the (3+1) dimensional DKP theory when the dynamics was restricted to one space dimension [10][11][12][13][14][15][16][17][18][19][20] , a finding sometimes referred to as a remarkable one. We argue that this is not surprising; indeed, it is a trivial consequence of our main result, since the equation for the unidimensional propagation of the dynamic components of the wave function in the (3+1) case should be formally identical to a (1+1)-dimensional DKP equation, which, as we have shown here, admits only a spin-0 representation.…”

Relativistic dynamics of a scalar boson confined by Woods–Saxon potential in anucleus

“…The DKP equation is used to obtain the relativistic dynamics of bosons subject to a variety of nonminimal vector coupling potentials. These potentials are not expressed in the Klein-Gordon equation [7,8].…”

On a Simple Relation between Duffin-Kemmer-Petiau and Tzou Algebras

“…The Duffin-Kemmer-Petiau (DKP) equations [1][2][3] have been gaining importance due to their applications to problems in particle and nuclear physics of spin 0 and spin 1 mesons [4][5][6][7][8][9][10][11][12][13][14][15]. Since spin 1 bosons can be also described by Hagen-Hurley equations [16][17][18] involving Tzou algebra [19][20][21], relations between DKP and Tzou algebras deserve a separate study.…”