The asymptotic behavior of the Klein-Gordon equation with external potential
Let U 0( t) and U( t) denote the temporal propagator of the Klein-Gordon equation □ ϑ = m 2 ϑ and the perturbed equation □ ϑ = ( m 2 + V( x)) ϑ, respectively. If (i) V ϵ L p ( E 3) for any 2 ⩽ p </ 3, (ii) V is real-valued and (iii) satisfies a restriction on the size of its negative part, then t...
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| Published in | Journal of mathematical analysis and applications Vol. 31; no. 2; pp. 334 - 348 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
01.01.1970
|
| Online Access | Get full text |
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| Summary: | Let
U
0(
t) and
U(
t) denote the temporal propagator of the Klein-Gordon equation □
ϑ =
m
2
ϑ and the perturbed equation □
ϑ = (
m
2 +
V(
x))
ϑ, respectively. If (i)
V
ϵ
L
p
(
E
3) for any 2 ⩽
p </ 3, (ii)
V is real-valued and (iii) satisfies a restriction on the size of its negative part, then the (free-to-physical) wave operators,
W
±: =
s − lim
U(−
t)
U
0(
t), as
t → ±∞ exist as bounded operators on the finite-energy and Lorentz-invariant solution space of the Klein-Gordon equation. |
|---|---|
| ISSN: | 0022-247X 1096-0813 |
| DOI: | 10.1016/0022-247X(70)90029-6 |