Authors
Citation
Y. Hu et G. Kallianpur, Schrodinger equations with fractional Laplacians, APPL MATH O, 42(3), 2000, pp. 281-290
Citations number
8
Categorie Soggetti
Mathematics
Journal title
APPLIED MATHEMATICS AND OPTIMIZATION
ISSN journal
00954616
→ ACNP
Volume
42
Issue
3
Year of publication
2000
Pages
281 - 290
Database
ISI
SICI code
0095-4616(200011/12)42:3<281:SEWFL>2.0.ZU;2-P
Abstract
It is shown that the unique solution of
{ partial derivative/partial derivativet Psi (t,x) = -(z(2))(alpha /2) (-De
lta)(alpha /2) Psi (t,x) + V(z,x)Psi (t,x), Psi (0,x) = f(x),
can be represented as
Psi (t,x) = Ef (x + (z)(1/alpha) X-s) exp { integral (t)(0) V(z,x + (z)(1/a
lpha) X-u) du},
where X = (X-t, t greater than or equal to 0) is a stable process whose gen
erator is (-Delta)(alpha /2) with X-0 = 0. AMS Classification. Primary 60H0
5, 60H10, Secondary 90A09, 90A12.