Geodesic
Free motion of $q$-deformed quantum particle
Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 1, pp. 87-93

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The paper considers $q$ deformation of the Heisenberg algebra and a representation for it by finite-difference operators. It is shown that for the automorphism of the algebra corresponding to free motion there does not exist a polynomial Harniltonian generating it. The propertiesofplanewaves, i.e., the eigenfunctions of the $q$-deformed momentum operator, are also considered. It is noted that for $q=\exp(\pi i\vartheta)$, where $\vartheta$ is irrational, the eigenfunctions can be umneasurable. 
@article{TMF_1992_93_1_a6,
     author = {S. V. Kozyrev},
     title = {Free motion of $q$-deformed quantum particle},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {87--93},
     publisher = {mathdoc},
     volume = {93},
     number = {1},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1992_93_1_a6/}
}
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S. V. Kozyrev. Free motion of $q$-deformed quantum particle. Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 1, pp. 87-93. http://geodesic.mathdoc.fr/item/TMF_1992_93_1_a6/