On essential self-adjointness of the relativistic hamiltonian of a spinless particle in a negative scalar potential
Ichinose, Wataru
Annales de l'I.H.P. Physique théorique, Tome 61 (1994), p. 241-252 / Harvested from Numdam
Publié le : 1994-01-01
@article{AIHPA_1994__60_2_241_0,
     author = {Ichinose, Wataru},
     title = {On essential self-adjointness of the relativistic hamiltonian of a spinless particle in a negative scalar potential},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {61},
     year = {1994},
     pages = {241-252},
     mrnumber = {1270297},
     zbl = {0791.47054},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1994__60_2_241_0}
}
Ichinose, Wataru. On essential self-adjointness of the relativistic hamiltonian of a spinless particle in a negative scalar potential. Annales de l'I.H.P. Physique théorique, Tome 61 (1994) pp. 241-252. http://gdmltest.u-ga.fr/item/AIHPA_1994__60_2_241_0/

[1] F.A. Berezin and M.A. Shubin, The Schrödinger Equation, Kluwer Academic Publishers, Dordrecht, Boston and London, 1991. | MR 1186643 | Zbl 0749.35001

[2] A.P. Calderón and R. Vaillancourt, On the Boundedness of Pseudo-Differential Operators, J. Math. Soc., Japan, Vol. 23, 1971, pp. 374-378. | MR 284872 | Zbl 0203.45903

[3] P.R. Chernoff, Schrödinger and Dirac Operators with Singular Potentials and Hyperbolic Equations, Pacific J. Math., Vol. 72, 1977, pp. 361-382. | MR 510049 | Zbl 0366.35031

[4] I. Daubechies, One Electron Molecules with Relativistic Kinetic Energy: Properties of the Discrete Spectrum, Commun. Math. Phys., Vol. 94, 1984, pp. 523-535. | MR 763750

[5] M.S.P. Eastham, W.D. Evans and J. B. McLEOD, The Essential Self-Adjointness of Schrödinger-Type Operators, Arch. Rational Mech. Anal., Vol. 60, 1976, pp. 185-204. | MR 417564 | Zbl 0326.35018

[6] W.G. Faris and R.B. Lavine, Commutators and Self-Adjointness of Hamiltonian Operators, Commun. Math. Phys., Vol. 35, 1974, pp. 39-48. | MR 391794 | Zbl 0287.47004

[7] I.W. Herbst, Spectral theory of the operator (p2+m2)1/2-Ze2/r, Ibid., Vol. 53, 1977, pp. 285-294. | MR 436854 | Zbl 0375.35047

[8] T. Ichinose, Essential Selfadjointness of the Weyl Quantized Relativistic Hamiltonian, Ann. Inst. Henri Poincaré, Phys. Théor., Vol. 51, 1989, pp. 265-298. | Numdam | MR 1034589 | Zbl 0721.35059

[9] T. Ichinose and T. Tsuchida, On Kato's Inequality for the Weyl Quantized Relativistic Hamiltonian, Manuscripta Math., Vol. 76, 1992, pp. 269-280. | MR 1185020 | Zbl 0767.35098

[10] W. Ichinose, Remarks on Self-Adjointness of Operators in Quantum Mechanics and h-dependency of Solutions for Their Cauchy Problem, Preprint.

[11] H. Kumano-Go, Pseudo-Differential Operators, M.I.T. Press, Cambridge, 1981.

[12] M. Nagase and T. Umeda, On the Essential Self-Adjointness of Pseudo-Differential Operators, Proc. Japan Acad. Série A, Vol. 64, 1988, pp. 94-97. | MR 966395 | Zbl 0669.35115

[13] M. Reed and B. Simon, Methods of Modern Mathematical Physics II, Fourier Analysis, Self-Adjointness, Academic Press, New York and London, 1975. | MR 493420 | Zbl 0308.47002

[14] M. Reed and B. Simon, Methods of Modern Mathematical Physics IV, Analysis of Operators, Academic Press, New York and London, 1978. | MR 493421 | Zbl 0401.47001

[15] M.A. Shubin, Pseudodifferential Operators and Spectral Theory, Springer-Verlag, Berlin and Heidelberg, 1987. | MR 883081 | Zbl 0616.47040

[16] R.A. Weder, Spectral Analysis of Pseudodifferential Operators, J. Functional Anal., Vol. 20, 1975, pp. 319-337. | MR 402547 | Zbl 0317.47035