  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. The existence of adelic matter at very high
energies is suggested.
