Geodesic
What Is a Quantum Stochastic Differential Equation from the Point of View of Functional Analysis?
Matematičeskie zametki, Tome 71 (2002) no. 3, pp. 448-469

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We prove that a quantum stochastic differential equation is the interaction representation of the Cauchy problem for the Schrödinger equation with Hamiltonian given by a certain operator restricted by a boundary condition. If the deficiency index of the boundary-value problem is trivial, then the corresponding quantum stochastic differential equation has a unique unitary solution. Therefore, by the deficiency index of a quantum stochastic differential equation we mean the deficiency index of the related symmetric boundary-value problem. In this paper, conditions sufficient for the essential self-adjointness of the symmetric boundary-value problem are obtained. These conditions are closely related to nonexplosion conditions for the pair of master Markov equations that we canonically assign to the quantum stochastic differential equation. 
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     author = {A. M. Chebotarev},
     title = {What {Is} a {Quantum} {Stochastic} {Differential} {Equation} from the {Point} of {View} of {Functional} {Analysis?}},
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A. M. Chebotarev. What Is a Quantum Stochastic Differential Equation from the Point of View of Functional Analysis?. Matematičeskie zametki, Tome 71 (2002) no. 3, pp. 448-469. http://geodesic.mathdoc.fr/item/MZM_2002_71_3_a10/