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We solve the generalized relativistic harmonic oscillator in 1+1 dimensions in the presence of a minimal length. Using the momentum space representation, we explore all the possible signs of the potentials and discuss their bound-state solutions for fermion and antifermions. Furthermore, we also find an isolated solution from the Sturm-Liouville scheme. All cases already analyzed in the literature, are obtained as particular cases.
We investigate the effective Dirac equation, corrected by merging two scenarios that are expected to emerge towards the quantum gravity scale. Namely, the existence of a minimal length, implemented by the generalized uncertainty principle, and exotic
The Levi-Civita transformation is applied in the two-dimensional (2D) Dirac and Klein-Gordon (KG) equations with equal external scalar and vector potentials. The Coulomb and harmonic oscillator problems are connected via the Levi-Civita transformatio
Growth of Young diagrams, equipped with Plancherel measure, follows the automodel equation of Kerov. Using the technology of unitary matrix model we show that such growth process is exactly same as the growth of gap-less phase in Gross-Witten and Wad
Solvability of the ubiquitous quantum harmonic oscillator relies on a spectrum generating osp(1|2) superconformal symmetry. We study the problem of constructing all quantum mechanical models with a hidden osp(1|2) symmetry on a given space of states.
We consider the self-adjoint extensions (SAE) of the symmetric supercharges and Hamiltonian for a model of SUSY Quantum Mechanics in $mathbb{R}^+$ with a singular superpotential. We show that only for two particular SAE, whose domains are scale invar