## Dept. of Mathematics and Computer Science (Berlin)

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**reviewer:** Miloslav Znojil
**reviewernum:** 9689

**revieweremail:** znojil@ujf.cas.cz

**zblno:** DE014404021

**author:** Grigoriu, Mircea

**shorttitle:** A local solution of the Schroedinger equation

**source:** J. Phys. A, Math. Gen. 31, No. 43, 8669 - 8676 (1998).

**rpclass:** 65C05

**rsclass:** 34F05

**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.

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