Quantum Coherence and the Nonlinear Schrödinger Equation
We show how the validity of Hamilton equation methods for determining the time evolution of trial state vectors in quantum mechanics may be tested. We show how an ansatz state vector consisting of a product of coherent states allows a differential operator to be constructed under which a scalar Hamilton function must be invariant. Since the Hamilton equations for the coherent state amplitudes are derived without approximation from the exact Heisenberg equations of motion for creation and annihilation operators, the differential invariance condition provides information about the admissibility of coherent state products as state vectors and the validity of the equations of motion subsequently derived.
KeywordsSoliton Coherence Lution
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