The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines

In this paper a microscopic quantum mechanical model of computers as represented by Turing machines is constructed. It is shown that for each number N and Turing machine Q there exists a Hamiltonian H _N ^Q and a class of appropriate initial states such that if c is such an initial state, then ψ _Q ^N (t)=exp(-1 H _N ^Q t) ψ _Q ^N (0) correctly describes at times t ₃, t ₆,⋯, t _3N model states that correspond to the completion of the first, second, ⋯, Nth computation step of Q. The model parameters can be adjusted so that for an arbitrary time interval Δ around t ₃, t ₆,⋯, t _3N, the "machine" part of ψ _Q ^N (t) is stationary.