Quantum mechanics on p-adic fields
- 1 December 1989
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 30 (12) , 2854-2874
- https://doi.org/10.1063/1.528468
Abstract
A formulation of quantum mechanics on p‐adic number fields is presented. Quantum amplitudes are taken as complex functions of p‐adic variables and it is shown how the Weyl approach to quantum mechanics can be generalized to the p‐adic case. The p‐adic analogs of simple one‐dimensional systems (free particle, compact and noncompact oscillators) are defined by a ‘‘group of motion,’’ which is an Abelian subgroup of SL (2,Qp). In each case the evolution operator is a unitary representation of the appropriate group. Its spectrum is given by characters and its eigenstates are calculated.Keywords
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