Unitary equivalence of Schrödinger and Heisenberg pictures survives in nonlinear quantum mechanics
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Diósi, Lajos
Institution: Eötvös Loránd University
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212004088