Document Type
Article
Publication Date
4-6-2026
Abstract
Quantum mechanics admits two distinct evolutions: deterministic unitary dynamics governed by the Schrödinger equation and the probabilistic collapse of the wave function. We show that the continuous collapse of a quantum state under measurement can, on a trajectory-by-trajectory basis, be equivalently described as unitary evolution generated by a time- and state-dependent Hermitian Hamiltonian with stochastic parameters. While the ensemble dynamics remains non-unitary, each individual trajectory thus admits a unitary representation. We derive explicit forms of such Hamiltonians for projective measurements on arbitrary n-level systems and for continuous position measurements of a harmonic oscillator, and we propose experimental schemes to test these predictions. Our framework provides a new approach to modeling and controlling continuously monitored quantum systems using only state-dependent unitary resources.
Recommended Citation
Hu, L., Jordan, A.N. Describing the wave function collapse process with a state-dependent Hamiltonian. Quantum Stud.: Math. Found. 13, 22 (2026). https://doi.org/10.1007/s40509-026-00394-x
Peer Reviewed
1
Copyright
The authors
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Comments
This article was originally published in Quantum Studies: Mathematics and Foundations, volume 13, in 2026. https://doi.org/10.1007/s40509-026-00394-x