Unitary equivalence of Schrödinger and Heisenberg pictures survives in nonlinear quantum mechanics

• URL: http://arxiv.org/abs/2609.07391v1
• Date: Mon, 07 Sep 2026 12:03:26 GMT
• Title: Unitary equivalence of Schrödinger and Heisenberg pictures survives in nonlinear quantum mechanics
• Abstract summary: equivalence of Schrdinger and Heisenberg pictures is often thought to break down in nonlinear quantum mechanics.<n>We show that for Hamiltonians depending on the state through instantaneous expectation values, the equivalence is preserved.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The equivalence of Schrödinger 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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