MR2351217
Tadayoshi ADACHI
Tadayoshi ADACHI
On the Mourre Estimates for Three Body Schrödinger Operators in a Constant Magnetic Field
Funkcialaj Ekvacioj. Serio Internacia
50
2007
339--370
http://fe.math.kobe-u.ac.jp/FE/FullPapers/50-2/50_339.pdf
http://www.ams.org/mathscinet-getitem?mr=MR2351217
We consider a three body quantum system in a constant magnetic field which has one neutral and two charged particles. Then we prove the existence of a conjugate operator and the Mourre estimate for the Hamiltonian which governs the system under the assumption that the total charge of the system is nonzero. The construction of a conjugate operator depends on the space dimension.
Mourre estimate, Three body problem, Constant magnetic field.
Primary 81U10; Secondary 81V70.
50-339
2007
On the Mourre Estimates for Three Body Schrödinger Operators in a Constant Magnetic Field
Tadayoshi ADACHI
Tadayoshi ADACHI
1
Adachi, T.
Scattering theory for a two-body quantum system in a constant magnetic field
J. Math. Sci., The Univ. of Tokyo
8
2001
243-274
MR1837164
2
Adachi, T.
On spectral and scattering theory for $N$-body Schrödinger operators in a constant magnetic field
Rev. in Math. Phys.
14
2002
199-240
MR1883557
3
Amrein, W. O.; Boutet de Monvel, A.; Georgescu, V.
$C_0$-groups, commutator methods and spectral theory of $N$-body Hamiltonians
Birkhäuser Verlag
1996
MR1388037
4
Avron, J.; Herbst, I. W.; Simon, B.
Schrödinger operators with magnetic fields. I. General interactions
Duke Math. J.
45
1978
847-883
MR0518109
5
Avron, J.; Herbst, I. W.; Simon, B.
Separation of center of mass in homogeneous magnetic fields
Ann. Phys.
114
1978
431-451
MR0507741
6
Cycon, H.; Froese, R. G.; Kirsch, W.; Simon, B.
Schrödinger Operators with Application to Quantum Mechanics and Global Geometry
Springer-Verlag
1987
MR0883643
7
DereziŅski, J.
Asymptotic completeness of long-range $N$-body quantum systems
Ann. of Math.
138
1993
427-476
MR1240577
8
DereziŅski, J.; Gérard, C.
Scattering Theory of Classical and Quantum $N$-Particle Systems
Springer-Verlag
1997
MR1459161
9
Froese, R.; Herbst, I. W.
A new proof of the Mourre estimate
Duke Math. J.
49
1982
1075-1085
MR0683011
10
Georgescu, V.; Gérard, C.
On the virial theorem in quantum mechanics
Commun. Math. Phys.
208
1999
275-281
MR1729087
11
Gérard, C.; Łaba, I.
Scattering theory for $N$-particle systems in constant magnetic fields
Duke Math. J.
76
1994
433-465
MR1302320
12
Gérard, C.; Łaba, I.
Scattering theory for $N$-particle systems in constant magnetic fields, II. Long-range interactions
Commun. P. D. E.
20
1995
1791-1830
MR1349232
13
Gérard, C.; Łaba, I.
Scattering theory for $3$-particle systems in constant magnetic fields: Dispersive case
Ann. Inst. Fourier, Grenoble
46
1996
801-876
MR1411729
14
Gérard, C.; Łaba, I.
Multiparticle Quantum Scattering in Constant Magnetic Fields
AMS
2002
MR1871447
15
Graf, G. M.
Asymptotic completeness for $N$-body short-range quantum systems: a new proof
Commun. Math. Phys.
132
1990
73-101
MR1069201
16
Jensen, A.; Nakamura, S.
The 2D Schrödinger equation for a neutral pair in a constant magnetic field
Ann. Inst. Henri Poincaré - Phys. Théor.
67
1997
387-410
MR1632236
17
Łaba, I.
Scattering for hydrogen-like systems in a constant magnetic field
Commun. P. D. E.
20
1995
741-762
MR1326905
18
Łaba, I.
Multiparticle quantum systems in constant magnetic fields
in Multiparticle quantum scattering with applications to nuclear, atomic and molecular physics (Minneapolis, MN, 1995) IMA Vol. Math. Appl., 89, Springer-Verlag
1997
147-215
MR1487921
19
Mourre, E.
Absence of singular continuous spectrum for certain self-adjoint operators
Commun. Math. Phys.
78
1981
391-408
MR0603501
20
Perry, P.; Sigal, I. M.; Simon, B.
Spectral analysis of $N$-body Schrödinger operators
Ann. of Math.
114
1981
517-567
MR0634428
21
Reed, M.; Simon, B.
Methods of Modern Mathematical Physics, I
Academic Press
1972
MR0493419
22
Reed, M.; Simon, B.
Methods of Modern Mathematical Physics, II
Academic Press
1975
MR0493420
23
Reed, M.; Simon, B.
Methods of Modern Mathematical Physics, III
Academic Press
1979
MR0529429
24
Reed, M.; Simon, B.
Methods of Modern Mathematical Physics, IV
Academic Press
1978
MR0493421
25
Skibsted, E.
Propagation estimates for $N$-body Schroedinger Operators
Commun. Math. Phys.
142
1991
67-98
MR1137775
26
Skibsted, E.
On the asymptotic completeness for particles in constant electromagnetic fields
in Partial differential equations and mathematical physics (Copenhagen, 1995; Lund, 1995) Progr. Nonlinear Differential Equations Appl., 21, Birkhäuser
1996
286-320
MR1380998
27
Skibsted, E.
Asymptotic completeness for particles in combined constant electric and magnetic fields, II
Duke Math. J.
89
1997
307-350
MR1460625