Effects of Lorentz symmetry violation on a spin-(1/2) neutral particle in a doubly anharmonic potential

Abstract We investigate the quantum dynamics of a spin-(1/2) neutral particle under the effects of Lorentz symmetry violation, characterized by a fixed time-like background vector and azimuthal electric fields added to the potential of a pure quartic oscillator. These effects, induced by the background vector that defines a preferred spacetime direction, modify the dynamics of the spin-(1/2) neutral particle and give rise to a doubly anharmonic oscillator-like potential. The main challenge is to find analytical solutions to the Schrödinger equation, considering that this nonlinear potential models realistic quantum physics scenarios. Finally, we obtain bound-state solutions in the nonrelativistic limit for the Schrödinger-Pauli equation of a spin-(1/2) neutral particle. An interesting quantum effect is observed: the constant associated with the pure quartic oscillator term is quantized, meaning it depends on the system's quantum numbers.