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Describing the wave function collapse process with a state-dependent Hamiltonian
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DOI：10.1007/s40509-026-00394-x.png)
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Abstract
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Quantum mechanics admits two distinct evolutions: deterministic unitary dynamics governed by the Schr & ouml;dinger 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.
Keywords:
Wave function collapse
Continuous quantum measurement
Quantum trajectories
Quantum control
Schr & ouml
dinger equation inverse problem
State-dependent Hamiltonian
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1
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26
Citations:
222
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