On Generalized Functions in Adelic Quantum Mechanics

Details On Generalized Functions in Adelic Quantum Mechanics On Generalized Functions in Adelic Quantum Mechanics

2004-04-29

arxiv.org/abs/math-ph/0404076v1

Integral Transform. Spec. Funct. 6 (1998) 197-2003

Physics

Mathematical Physics

9pages

Scientific paper

Some aspects of adelic generalized functions, as linear continuous functionals on the space of Schwartz-Bruhat functions, are considered. The importance of adelic generalized functions in adelic quantum mechanics is demonstrated. In particular, adelic product formula for Gauss integrals is derived, and the connection between the functional relation for the Riemann zeta function and quantum states of the harmonic oscillator is stated.

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