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ADELIC HARMONIC OSCILLATOR
International Journal of Modern Physics A
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 well known functional relation for the Riemann zeta function. Some expectation values are calculated.doi:10.1142/s0217751x95001145 fatcat:zmrwacplsfh7phsdlw4w76kqk4