Stochastic Schr?dinger Equation In Terms Of Local Quantum Bernoulli Noises

Quantum Bernoulli noises are the family of annihilation and creation operators acting on Bernoulli functionals,which satisfy a canonical anti-commutation relation(CAR)in equal-time.Local quantum Bernoulli noise is the family of local annihi-lation and creation operators,which is the localization of quantum Bernoulli noise and satisfies a local canonical anti-communication relation in equal-time.In this pa-per,we consider a linear stochastic Schr?dinger equation in terms of local quantum Bernoulli noise.First,we investigate a finite linear stochastic Schr?dinger equation in terms of local quantum Bernoulli noise,which has the existence and uniqueness of regular solution,we also study its priori estimates and finite dimensional approx-imation,as well as its numerical simulation.Next,we discuss the existence and uniqueness of regular solution to the general linear stochastic Schr?dinger equation by the local quantum Bernoulli noise.Our main results are as follows.Firstly,we discuss the existence and uniqueness of regular solution to finite linear stochastic Schr?dinger equation,and finite dimensional approximation.Secondly,we establish the numerical simulation of solution to finite linear s-tochastic Schr?dinger equation.Finally,we give the existence and uniqueness of regular solution to the general linear stochastic Schr?dinger equation.