Geodesic
$p$-Adic and adelic harmonic oscillator with a time-dependent frequency
Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 2, pp. 239-248

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The classical and quantum formalism for a $p$-adic and adelic harmonic oscillator with a time-dependent frequency is developed, and general formulas are obtained for the main theoretical quantities. In particular, the $p$-adic propagator is calculated, and the existence of a simple vacuum state as well as adelic quantum dynamics is shown. A spatial discreteness and a $p$-adic quantum mechanical phase are noted. 
@article{TMF_2000_124_2_a3,
     author = {G. S. Djordjevi\v{c} and B. G. Dragovich},
     title = {$p${-Adic} and adelic harmonic oscillator with a time-dependent frequency},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {239--248},
     publisher = {mathdoc},
     volume = {124},
     number = {2},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2000_124_2_a3/}
}
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G. S. Djordjevič; B. G. Dragovich. $p$-Adic and adelic harmonic oscillator with a time-dependent frequency. Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 2, pp. 239-248. http://geodesic.mathdoc.fr/item/TMF_2000_124_2_a3/