Relation of deformed nonlinear algebras with linear ones
arXiv:1312.5104 · doi:10.1088/1751-8113/47/2/025207
Abstract
The relation between nonlinear algebras and linear ones is established. For one-dimensional nonlinear deformed Heisenberg algebra with two operators we find the function of deformation for which this nonlinear algebra can be transformed to a linear one with three operators. We also establish the relation between Lie algebra of total angular momentum and corresponding nonlinear one. This relation gives a possibility to simplify and to solve the eigenvalue problem for the Hamiltonian in a nonlinear case using the reduction of this problem to the case of linear algebra. It is demonstrated on the example of harmonic oscillator.
17 pages
References in corpus (11)
- Universality of Quantum Gravity Corrections
- The effects of minimal length and maximal momentum on the transition rate of ultra cold neutrons in gravitational field
- Hydrogen-atom spectrum under a minimal-length hypothesis
- Minimal Length Uncertainty Relation and gravitational quantum well
- Minimal Length and Bouncing Particle Spectrum
- 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
- Dilaton Cosmology, Noncommutativity and Generalized Uncertainty Principle
- Scattering problem in deformed space with minimal length
- Quantum gravity, minimum length and Keplerian orbits
- The quantum N-body problem with a minimal length