Lower bounds for the spinless Salpeter equation

We obtain lower bounds on the ground state energy, in one and three dimensions, for the spinless Salpeter equation (Schrodinger equation with a relativistic kinetic energy operator) applicable to potentials for which the attractive parts are in

L^p(\R^n)

for some

p>n

(

n=1

or 3). An extension to confining potentials, which are not in

L^p(\R^n)

, is also presented.

Note:

In honor of Francesco Calogero on the occasion of his 70th birthday

References(40)

Figures(0)

A Relativistic equation for bound state problems

E.E. Salpeter
(
- Cornell U., LNS
)
,
H.A. Bethe
(
- Cornell U., LNS
)

- Phys.Rev. 84 (1951) 1232-1242
•
DOI:
- 10.1103/PhysRev.84.1232

Mesons in a Relativized Quark Model with Chromodynamics

S. Godfrey
(
- Toronto U.
)
,
Nathan Isgur
(
- Toronto U.
)

- Phys.Rev.D 32 (1985) 189-231,
- Phys. Rev. D32 ( 1985) 189-231
•
DOI:
- 10.1103/PhysRevD.32.189

Potential models and meson spectra

C. Semay
(
- UMH, Mons
)
,
B. Silvestre-Brac
(
- LPSC, Grenoble
)

- Nucl.Phys.A 618 (1997) 455-482
•
DOI:
- 10.1016/S0375-9474(97)00060-2

Light meson spectra and instanton induced forces

F. Brau
(
- UMH, Mons
)
,
C. Semay
(
- UMH, Mons
)

- Phys.Rev.D 58 (1998) 034015
•
e-Print:
- hep-ph/0412179
•
DOI:
- 10.1103/PhysRevD.58.034015

Unified description of light and strange baryon spectra

L.Ya. Glozman
(
- Graz U.
)
,
Willibald Plessas
(
- Graz U.
)
,
K. Varga
(
- Debrecen, Inst. Nucl. Res. and
- Wako, RIKEN
)
,
R.F. Wagenbrunn
(
- Graz U.
)

- Phys.Rev.D 58 (1998) 094030
•
e-Print:
- hep-ph/9706507
•
DOI:
- 10.1103/PhysRevD.58.094030

A Unified meson baryon potential

Fabian Brau
(
- UMH, Mons
)
,
Claude Semay
(
- UMH, Mons
)
,
Bernard Silvestre-Brac
(
- LPSC, Grenoble
)

- Phys.Rev.C 66 (2002) 055202
•
e-Print:
- hep-ph/0412176
•
DOI:
- 10.1103/PhysRevC.66.055202

Spectral Theory of the Operator p2 m1/2-Z e**2r

I.W. Herbst
(
- Princeton U.
)

- Commun.Math.Phys. 53 (1977) 285-294
•
DOI:
- 10.1007/BF01609852

Partial Wave Analysis of a Relativistic Coulomb Problem

P. Castorina
(
- Catania U. and
- INFN, Catania
)
,
P. Cea
(
- Bari U. and
- INFN, Bari
)
,
G. Nardulli
(
- Bari U. and
- INFN, Bari
)
,
G. Paiano
(
- Bari U. and
- INFN, Bari
)

- Phys.Rev.D 29 (1984) 2660
•
DOI:
- 10.1103/PhysRevD.29.2660

Relativistic Wave Equations in Momentum Space

G. Hardekopf
(
- Maryland U.
)
,
J. Sucher
(
- Maryland U.
)

- Phys.Rev.A 30 (1984) 703-711
•
DOI:
- 10.1103/PhysRevA.30.703

Critical coupling constants for relativistic wave equations and vacuum breakdown in quantum electrodynamics

- Phys.Rev.A 31 (1985) 4, 2020
•
DOI:
- 10.1103/PhysRevA.31.2020

Semirelativistic Stability and Critical Mass of a System of Spinless Bosons in Gravitational Interaction

Andre Martin
(
- CERN
)
,
S.M. Roy
(
- CERN
)

- Phys.Lett.B 233 (1989) 407-411
•
DOI:
- 10.1016/0370-2693(89)91331-2

The 'Herbst Hamiltonian' and the mass of boson stars

- Phys.Lett.B 320 (1994) 105-109
•
DOI:
- 10.1016/0370-2693(94)90831-1

Energy bounds for the spinless Salpeter equation: Harmonic oscillator

Richard L. Hall
(
- Concordia U., Montreal
)
,
Wolfgang Lucha
(
- Vienna, OAW
)
,
Franz F. Schoberl
(
- Vienna U.
)

- J.Phys.A 34 (2001) 5059-5064
•
e-Print:
- hep-th/0012127
•
DOI:
- 10.1088/0305-4470/34/24/304

Energy bounds for the spinless Salpeter equation

Richard L. Hall
(
- Concordia U., Montreal
)
,
Wolfgang Lucha
(
- Vienna, OAW
)
,
F.F. Schoberl
(
- Vienna U.
)

- J.Math.Phys. 42 (2001) 5228-5237
•
e-Print:
- hep-th/0101223
•
DOI:
- 10.1063/1.1405848

Discrete spectra of semirelativistic Hamiltonians from envelope theory

Richard L. Hall
(
- Concordia U., Montreal
)
,
Wolfgang Lucha
(
- Vienna, OAW
)
,
Franz F. Schoberl
(
- Vienna U.
)

- Int.J.Mod.Phys.A 17 (2002) 1931-1952
•
e-Print:
- hep-th/0110220
•
DOI:
- 10.1142/S0217751X02010522

Discrete spectra of semirelativistic Hamiltonians

Richard L. Hall
(
- Concordia U., Montreal
)
,
Wolfgang Lucha
(
- Vienna, OAW
)
,
Franz F. Schoberl
(
- Vienna U.
)

- Int.J.Mod.Phys.A 18 (2003) 2657-2680
•
e-Print:
- hep-th/0210149
•
DOI:
- 10.1142/S0217751X0301406X

- Proc.Nat.Acad.Sci.A 38 961

- Proc.Nat.Acad.Sci.A 47 122

- Commun.Math.Phys. 1 80

- Nuovo Cim.A 58 191

Rigorous lower bounds on the energies of the N -body problem

R.L. Hall

- Phys.Lett.B 30 (1969) 320-321
•
DOI:
- 10.1016/0370-2693(69)90491-2

An Inequality on S-Wave Bound States with Correct Coupling Constant Dependence

Andre Martin
(
- CERN
)

- Commun.Math.Phys. 55 (1977) 293
•
DOI:
- 10.1007/BF01614552

- J.Phys.A 11 55

Improved Lower Bounds for the n Fermion Problem

M.R. Manning
(
- New Zealand, Inst. Nucl. Sci.
)

- J.Phys.A 11 (1978) 855-869
•
DOI:
- 10.1088/0305-4470/11/5/016

- J.Phys.A 12 459

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