Abstract
We consider the simplest case of two nonlinear quantum eigenstates whose overlap integral defined by their inner product is non-zero. We propose to regard this nonlinear system as a mixed-state quantum system obtained by statistically combining the two nonlinear eigenstates with appropriate normalized probabilities. Since this description in terms of the density operator is unambiguous only if the quantum states of the mixture are orthonormal, we use Löwdin’s change of basis to symmetrically orthonormalize the original pair of non-orthogonal (since nonlinear) eigenstates and to define the corresponding density matrix. We show by simple examples that this mixed-state description of a nonlinear quantum system is in good agreement with experimental and/or numerical results.
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