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Energy levels corresponding to $$p$$-adic quantum states. (English. Russian original) Zbl 0879.46038
Dokl. Math. 51, No. 3, 452-455 (1995); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 342, No. 5, 603-606 (1995).
Hamiltonians of a harmonic oscillator with a constant potential are considered. A number of other models were studied by the authors in the paper [Int. J. Theor. Phys. 33, No. 6, 1217-1228 (1994; Zbl 0842.60096)].
The following theorem is proved: Let $$|\lambda+ 1|_p<|2|^3_p p^{3/(1-p)}$$. Then the Hermitian coefficients $$J(2s)$$ tend to zero in $$Q_p$$ as $$s\to\infty$$.

##### MSC:
 46N50 Applications of functional analysis in quantum physics 46S10 Functional analysis over fields other than $$\mathbb{R}$$ or $$\mathbb{C}$$ or the quaternions; non-Archimedean functional analysis 60K40 Other physical applications of random processes