dorsal/arxiv
View SchemaStructure and Properties of Hughston's Stochastic Extension of the Schr\"odinger Equation
| Authors | Stephen L. Adler, Lawrence P. Horwitz |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9909026 |
| URL | https://arxiv.org/abs/quant-ph/9909026 |
| DOI | 10.1063/1.533255 |
Abstract
Hughston has recently proposed a stochastic extension of the Schr\"odinger equation, expressed as a stochastic differential equation on projective Hilbert space. We derive new projective Hilbert space identities, which we use to give a general proof that Hughston's equation leads to state vector collapse to energy eigenstates, with collapse probabilities given by the quantum mechanical probabilities computed from the initial state. We discuss the relation of Hughston's equation to earlier work on norm-preserving stochastic equations, and show that Hughston's equation can be written as a manifestly unitary stochastic evolution equation for the pure state density matrix. We discuss the behavior of systems constructed as direct products of independent subsystems, and briefly address the question of whether an energy-based approach, such as Hughston's, suffices to give an objective interpretation of the measurement process in quantum mechanics.
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"abstract": "Hughston has recently proposed a stochastic extension of the Schr\\\"odinger\nequation, expressed as a stochastic differential equation on projective Hilbert\nspace. We derive new projective Hilbert space identities, which we use to give\na general proof that Hughston\u0027s equation leads to state vector collapse to\nenergy eigenstates, with collapse probabilities given by the quantum mechanical\nprobabilities computed from the initial state. We discuss the relation of\nHughston\u0027s equation to earlier work on norm-preserving stochastic equations,\nand show that Hughston\u0027s equation can be written as a manifestly unitary\nstochastic evolution equation for the pure state density matrix. We discuss the\nbehavior of systems constructed as direct products of independent subsystems,\nand briefly address the question of whether an energy-based approach, such as\nHughston\u0027s, suffices to give an objective interpretation of the measurement\nprocess in quantum mechanics.",
"arxiv_id": "quant-ph/9909026",
"authors": [
"Stephen L. Adler",
"Lawrence P. Horwitz"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.533255",
"title": "Structure and Properties of Hughston\u0027s Stochastic Extension of the Schr\\\"odinger Equation",
"url": "https://arxiv.org/abs/quant-ph/9909026"
},
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