On the attractive inverse-square potential in the induced electric dipole system under the influence of the harmonic oscillator

Abstract

We obtain the analytical solutions to the Schr\"odinger equation for the the attractive inverse-square potential in an induced electric dipole moment system under the influence of the harmonic oscillator. We show that bound states can exist when the electric field configuration brings a cut-off point that imposes a forbidden region for the neutral particle. Then, by dealing with $s$-waves, we obtain the energy eigenvalues in the strong electric field regime and for small values of the angular frequency of the harmonic oscillator. Further, we extend our discussion about the energy eigenvalues beyond the $s$-waves.

Lorentz Symmetry Violation Effects Caused by the Coupling between the Field fμγ5 and the Derivative of the Fermionic Field on One-Dimensional Potentials

“…We thus search for Lorentz symmetry violation effects on a particle subject to a quantum bouncer [40][41][42], the attractive inverse-square potential [44], a modified attractive inverse-square potential [50], and the scalar exponential potential [41,45]. Despite working with (1 + 1)-dimensions, we should observe that these potentials can be dealt with by using the spherical and cylindrical symmetries.…”

“…where we also have > 0 and a > 0. Recently, we studied an analogue of the potential (32) in a system of a neutral particle with an induced electric dipole moment [50].…”

“…where c 1 and c 2 are constants. The functions M κ, iµ (r) and W κ, iµ (r) are the Whittaker functions of first and second kinds of imaginary order, respectively [50,76]. Besides, the parameters κ and µ are defined as…”

“…Let us impose that u(r) → 0 when r → ∞. Thereby, let us take c 1 = 0 in Equation ( 36), and thus, the solution to Equation ( 35) can be given in terms of the Whittaker functions of second kind of imaginary order [50,76]:…”