Abstract
Quantum mechanical Hamiltonians of the form of n harmonic oscillators coupled via an interaction of the form ε times a polynomial in the position and momenta variables are studied in a rigorous Hilbert space setting. In particular, normal form theory is used to define the mth approximation to the associated Schrödinger initial value problem and it is shown that it deviates in norm from the exact solution by a term of order εm+1 ‖t‖ (t=time) provided only that the initial vector is confined to an appropriate dense subspace. The main concentration is on the case in which there exist no resonances of order ≤m between the frequencies of the n oscillators, but the case of two oscillators in 1:1 resonance is also taken up.
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