ADELIC HARMONIC OSCILLATOR

Adelic Harmonic Oscillator

Using the Weyl quantization we formulate one-dimensional adelic quantum mechanics, which unifies and treats ordinary and p-adic quantum mechanics on an equal footing. As an illustration the corresponding harmonic oscillator is considered. It is a simple, exact and instructive adelic model. Eigenstates are Schwartz-Bruhat functions. The Mellin transform of a simplest vacuum state leads to the we...

Adelic Model of Harmonic Oscillator

Adelic quantum mechanics is formulated. The corresponding model of the harmonic oscillator is considered. The adelic harmonic oscillator exhibits many interesting features. One of them is a softening of the uncertainty relation.

p-ADIC AND ADELIC HARMONIC OSCILLATOR WITH TIME-DEPENDENT FREQUENCY

In quantum-mechanical experiments, as well as in all measurements, numerical results belong to the field of rational numbers Q. In principle, the corresponding theoretical models could be made using only Q, but it would missed usual effectiveness and beauty of mathematical analysis. So, instead of Q one traditionally applies the field of real numbers R in classical mechanics and the field of co...

Harmonic analysis over adelic spaces

In [4], D. Osipov and A. Parshin developed an approach to harmonic analysis on higher dimensional local fields through categories of filtered vector spaces as in [3]. In the present paper we give a variant of this approach that behaves nicely for inductive arguments. We establish Pontryagin duality, the Fourier inversion formula, and a Plancherel formula for all dimensions. ∗This paper was writ...

Harmonic Oscillator