On Macroscopic Energy Gap for q -Quantum Mechanical Systems
Abstract
The q-deformed harmonic oscillator within the framework of the recently introduced Schwenk-Wess
q
-Heisenberg algebra is considered. It is shown, that for "physical" values
q∼1
, the gap between the energy levels decreases with growing energy. Comparing with the other (real)
q
-deformations of the harmonic oscillator, where the gap instead increases, indicates that the formation of the macroscopic energy gap in the Schwenk-Wess
q
-Quantum Mechanics may be avoided.