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arXiv · 2609.07391

Unitary equivalence of Schr\"odinger and Heisenberg pictures survives in nonlinear quantum mechanics

Lajos Diósi
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Abstract

The equivalence of Schr\"odinger and Heisenberg pictures is often thought to break down in nonlinear quantum mechanics due to the absence of a state-independent unitary propagator. We show that for Hamiltonians depending on the state through instantaneous expectation values, the equivalence is preserved. While the unitary intertwiner becomes initial-state dependent, it remains well-defined and ensures identical physical predictions in both pictures. We illustrate this with the analytically solvable examples of a nonlinear spin precession and a mean-field harmonic force, as well as in local field theory with mean-field coupling.

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Lajos Diósi. 2026-09-07. Unitary equivalence of Schr\"odinger and Heisenberg pictures survives in nonlinear quantum mechanics. https://arxiv.org/abs/2609.07391

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