We construct the exact position representation for a deformed (non-relativistic) quantum mechanics which exhibits an intrinsic maximum momentum and use it to study problems such as a particle in a box and an asymmetric well. In particular, we show that unlike usual quantum mechanics, the present deformed case delays the formation of bound states in a finite potential well, a distinguishing feature that might be relevant for empirical investigations. We also contrast our results with the string-motivated type of deformed quantum mechanics which incorporates a minimum position uncertainty rather than a maximum momentum.We construct the exact position representation for a deformed (non-relativistic) quantum mechanics which exhibits an intrinsic maximum momentum and use it to study problems such as a particle in a box and an asymmetric well. In particular, we show that unlike usual quantum mechanics, the present deformed case delays the formation of bound states in a finite potential well, a distinguishing feature that might be relevant for empirical investigations. We also contrast our results with the string-motivated type of deformed quantum mechanics which incorporates a minimum position uncertainty rather than a maximum momentum.

Modern Physics Letters AMay 10, 201311 citations

QUANTUM-MECHANICAL GENERATORS OF THE GROUP O

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FOR HYDROGEN- ATOM BOUND STATES