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

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.

arXiv:2609.07391 [quant-ph]

(or arXiv:2609.07391v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.07391 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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