Exactly solvable problems in the momentum space with a minimum uncertainty in position

Abstract

A new approach in solution of simple quantum mechanical problems in deformed space with minimal length is presented. We propose the generalization of Schroëdinger equation in momentum representation on the case of deformed Heisenberg algebra with minimal length. Assuming that the kernel of potential energy operator do not change in the case of deformation, we obtain exact solution of eigenproblem of a particle in delta potential as well as double delta potential. Particle in Coulomb like potential is revisited and the problem of inversibility and hermicity of inverse coordinate operator is solved.

References in corpus (4)

• Hydrogen-atom spectrum under a minimal-length hypothesis
• Corrections to the ns-levels of hydrogen atom in deformed space with minimal length
• Singular inverse square potential in arbitrary dimensions with a minimal length: Application to the motion of a dipole in a cosmic string background
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Cited by in corpus (10)

• Cosmological Horizons, Uncertainty Principle and Maximum Length Quantum Mechanics
• Singular inverse square potential in coordinate space with a minimal length
• One-dimensional Coulomb-like problem in general case of deformed space with minimal length
• Dirac $\delta$-function potential in quasiposition representation of a minimal-length scenario
• Exact solutions for two-body problems in 1D deformed space with minimal length
• Integral Transforms and $\mathcal{P}\mathcal{T}$-symmetric Hamiltonians
• Regularization of ${\delta }^{\prime }$ potential in general case of deformed space with minimal length
• Tunneling dynamics of the relativistic Schrodinger/Salpeter equation
• Quantum speed limit as a sensitive probe of Planck-scale effects
• Exact continuity equation in a space with minimal length