Quantum Coherence and the Nonlinear Schrödinger Equation

  • D. W. Brown
  • K. Lindenberg
  • B. J. West
Conference paper
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 69)


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.


Coherent State Hamilton Function Hamiltonian Operator Hamilton Equation Defense Advance Research Project Agency 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • D. W. Brown
    • 1
  • K. Lindenberg
    • 1
  • B. J. West
    • 2
  1. 1.Department of Chemistry B-014University of CaliforniaSan Diego, La JollaUSA
  2. 2.Division of Applied Nonlinear ProblemsLa Jolla InstituteLa JollaUSA

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