caa a22 4500 467911592 CHVBK 20180406152850.0 cr unu---uuuuu 170328e20060501xx s 000 0 eng 10.1007/s11232-006-0072-y doi (NATIONALLICENCE)springer-10.1007/s11232-006-0072-y The q -deformed harmonic oscillator, coherent states, and the uncertainty relation [Elektronische Daten] [V. Eremin, A. Meldianov] For a q-deformed harmonic oscillator, we find explicit coordinate representations of the creation and annihilation operators, eigenfunctions, and coherent states (the last being defined as eigenstates of the annihilation operator). We calculate the product of the "coordinate-momentum” uncertainties in q-oscillator eigenstates and in coherent states. For the oscillator, this product is minimum in the ground state and equals 1/2, as in the standard quantum mechanics. For coherent states, the q-deformation results in a violation of the standard uncertainty relation; the product of the coordinate-and momentum-operator uncertainties is always less than 1/2. States with the minimum uncertainty, which tends to zero, correspond to the values of λ near the convergence radius of the q-exponential. Springer Science+Business Media, Inc., 2006 q -deformation nationallicence harmonic oscillator nationallicence creation operators nationallicence annihilation operators nationallicence coherent states nationallicence uncertainty relation nationallicence Eremin V. Moscow State University, Moscow, Russia aut Meldianov A. Moscow State University, Moscow, Russia aut Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 147/2(2006-05-01), 709-715 0040-5779 147:2<709 2006 147 11232 https://doi.org/10.1007/s11232-006-0072-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11232-006-0072-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Eremin V. Moscow State University, Moscow, Russia aut NATIONALLICENCE 700 1- Meldianov A. Moscow State University, Moscow, Russia aut NATIONALLICENCE 773 0- Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 147/2(2006-05-01), 709-715 0040-5779 147:2<709 2006 147 11232 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer