Exact solutions for two-body problems in 1D deformed space with minimal length

Abstract

We reduce two-body problem to the one-body problem in general case of deformed Heisenberg algebra leading to minimal length.Two-body problems with delta and Coulomb-like interactions are solved exactly. We obtain analytical expression for the energy spectrum for partial cases of deformation function. The dependence of the energy spectrum on the center-of-mass momentum is found. For special case of deformation function, which correspondes to cutoff procedure in momentum space it is shown that this dependence is more likely to observe for identical particles.

References in corpus (30)

• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• A Generalized Uncertainty Principle in Quantum Gravity
• Nonpointlike Particles in Harmonic Oscillators
• Minimal Length Uncertainty Relation and Hydrogen Atom
• Uncertainty Relation in Quantum Mechanics with Quantum Group Symmetry
• Exact Solution of the Harmonic Oscillator in Arbitrary Dimensions with Minimal Length Uncertainty Relations
• Short Distance vs. Long Distance Physics: The Classical Limit of the Minimal Length Uncertainty Relation
• Maximal Localisation in the Presence of Minimal Uncertainties in Positions and Momenta
• Dirac oscillator with nonzero minimal uncertainty in position
• Hydrogen-atom spectrum under a minimal-length hypothesis
• Composite system in deformed space with minimal length
• Lorentz-covariant deformed algebra with minimal length and application to the 1+1-dimensional Dirac oscillator
• Regularization of the Singular Inverse Square Potential in Quantum Mechanics with a Minimal length
• Perturbation hydrogen-atom spectrum in deformed space with minimal length
• Harmonic oscillator with minimal length uncertainty relations and ladder operators
• One dimensional Coulomb-like problem in deformed space with minimal length
• Deformed Heisenberg algebra with minimal length and equivalence principle
• Corrections to the ns-levels of hydrogen atom in deformed space with minimal length
• Harmonic oscillator with nonzero minimal uncertainties in both position and momentum in a SUSYQM framework
• Composite system in noncommutative space and the equivalence principle
• More on a SUSYQM approach to the harmonic oscillator with nonzero minimal uncertainties in position and/or momentum
• Singular inverse square potential in arbitrary dimensions with a minimal length: Application to the motion of a dipole in a cosmic string background
• Weak equivalence principle in noncommutative phase space and the parameters of noncommutativity
• Conformal Invariance in noncommutative geometry and mutually interacting Snyder Particles
• Orbital magnetic moment of the electron in the hydrogen atom in deformed space with minimal length
• Deformed Heisenberg algebra and minimal length
• Effect of coordinate noncommutativity on the mass of a particle in a uniform field and the equivalence principle
• Exactly solvable problems in the momentum space with a minimum uncertainty in position
• Light baryon masses in different large-$N_c$ limits
• One-dimensional Coulomb-like problem in general case of deformed space with minimal length

Cited by in corpus (2)

• Regularization of ${\delta }^{\prime }$ potential in general case of deformed space with minimal length
• Exact continuity equation in a space with minimal length