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In this page, I write exact solutions of
Energy Representation of Uda Equation (1).

Any unentangled solution is functional Φ such that

where ∀n ∈ Z; cnC.

The quantum history represented by this solution is the same history as represented by wave function ψ such that
ψ(n, t) = exp(-iωtn + cn) = λn exp(-iωnt)
in the old grammar.
λn ≡ exp(cn).
If A†A|n> = n|n>, Σn=0 ψ(n, t)|n> = Σn=0 λnexp(-iωnt)|n>, Σn=0 ψ(n, 0)|n> = Σn=0 λn|n>.

Of course, any superposition of unentangled solutions is also a solution.
Moreover, any entangled solution perhaps is a superposition of unentangled solutions.
It is functional Φ such that

where ∀n ∈ Z; anR and bnR and f(a0, b0, a1, b1, a2, b2, ・・・) ∈ C.

cn = an + ibn, λn = exp(an + ibn).

Normalization condition for initial state is that

To let the integral converge, b and ν is restricted.
However, I do not put such a condition because there is no ambiguity even if the integral diverges.

The content of this page was developed in
Number Representation of Uda Equation @ Quantum History Theory @ Problems.

Author Yuichi Uda, Write start at 2019/11/08/17:22JST, Last edit at 2019/11/22/18:45JST