Eigenvalue problems in quantum mechanics with deformed Heisenberg algebra

Abstract:
Quantum systems with deformed Heisenberg algebra leading to noncommutative space arise in many branches of physics: string theory and general relativity, coordinate noncommutativity in the lowest Landau levels, quantum motion of the particle with a position-dependent effective mass, etc. We study eigenvalue problems in quantum mechanics with deformed Heisenberg algebra in the particular case, which leads to quantum space with nonzero minimal uncertainties in position and momentum. Using supersymmetric quantum mechanics with shape invariancy (factorization method) we obtain exact solution of the eigenvalue problem for some quantum systems with deformed Heisenberg algebra.