Department for Theoretical Physics,

Ivan Franko Lviv National University,

12 Drahomanov Str.,

Lviv, UA-79005,

UKRAINE

E-mail: tkachuk@ktf.franko.lviv.ua

**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.