author: Grigoriu, Mircea
shorttitle: A local solution of the Schroedinger equation
source: J. Phys. A, Math. Gen. 31, No. 43, 8669 - 8676 (1998).
keywords: diffusion processes, Ito formula, Monte Carlo simulation, Schroedinger-type ordinary differential eigenvalue problem
revtext: Monte Carlo methods often employ the statistical simulation of desired quantities via Brownian motion and Ito calculus. Their sample is presented (cf. the key formula (15)), illustrated (via two examples in section V) and discussed. It is a bit unfortunate that the method is characterized as simple, accurate and general. It is also quite confusing that this type of an interesting though, apparently, rather academic methodical proposal is given the misleading title which promises ``a local solution" (of course, formula (15) holds at a single value of the coordinate, but it still requires an integration over ``times"). Finally, I do not see any persuasive reason why the time-independent ordinary differential equation in question should be called ``Schroedinger". From the point of view of quantum mechanics, both illustrations using just zero energy and a constant potential on a finite interval look extremely artificial.