On essential self-adjointness of the relativistic hamiltonian of a spinless particle in a negative scalar potential

Wataru Ichinose

Annales de l'I.H.P. Physique théorique (1994)

  • Volume: 60, Issue: 2, page 241-252
  • ISSN: 0246-0211

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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 60.2 (1994): 241-252. <http://eudml.org/doc/76634>.

@article{Ichinose1994,
author = {Ichinose, Wataru},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {relativistic quantum hamiltonian; spinless particle in an electromagnetic field; Weyl correspondence; essentially selfadjoint; Dirac equation; commutator theorem},
language = {eng},
number = {2},
pages = {241-252},
publisher = {Gauthier-Villars},
title = {On essential self-adjointness of the relativistic hamiltonian of a spinless particle in a negative scalar potential},
url = {http://eudml.org/doc/76634},
volume = {60},
year = {1994},
}

TY - JOUR
AU - Ichinose, Wataru
TI - On essential self-adjointness of the relativistic hamiltonian of a spinless particle in a negative scalar potential
JO - Annales de l'I.H.P. Physique théorique
PY - 1994
PB - Gauthier-Villars
VL - 60
IS - 2
SP - 241
EP - 252
LA - eng
KW - relativistic quantum hamiltonian; spinless particle in an electromagnetic field; Weyl correspondence; essentially selfadjoint; Dirac equation; commutator theorem
UR - http://eudml.org/doc/76634
ER -

References

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  1. [1] F.A. Berezin and M.A. Shubin, The Schrödinger Equation, Kluwer Academic Publishers, Dordrecht, Boston and London, 1991. Zbl0749.35001MR1186643
  2. [2] A.P. Calderón and R. Vaillancourt, On the Boundedness of Pseudo-Differential Operators, J. Math. Soc., Japan, Vol. 23, 1971, pp. 374-378. Zbl0203.45903MR284872
  3. [3] P.R. Chernoff, Schrödinger and Dirac Operators with Singular Potentials and Hyperbolic Equations, Pacific J. Math., Vol. 72, 1977, pp. 361-382. Zbl0366.35031MR510049
  4. [4] I. Daubechies, One Electron Molecules with Relativistic Kinetic Energy: Properties of the Discrete Spectrum, Commun. Math. Phys., Vol. 94, 1984, pp. 523-535. MR763750
  5. [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. Zbl0326.35018MR417564
  6. [6] W.G. Faris and R.B. Lavine, Commutators and Self-Adjointness of Hamiltonian Operators, Commun. Math. Phys., Vol. 35, 1974, pp. 39-48. Zbl0287.47004MR391794
  7. [7] I.W. Herbst, Spectral theory of the operator (p2+m2)1/2-Ze2/r, Ibid., Vol. 53, 1977, pp. 285-294. Zbl0375.35047MR436854
  8. [8] T. Ichinose, Essential Selfadjointness of the Weyl Quantized Relativistic Hamiltonian, Ann. Inst. Henri Poincaré, Phys. Théor., Vol. 51, 1989, pp. 265-298. Zbl0721.35059MR1034589
  9. [9] T. Ichinose and T. Tsuchida, On Kato's Inequality for the Weyl Quantized Relativistic Hamiltonian, Manuscripta Math., Vol. 76, 1992, pp. 269-280. Zbl0767.35098MR1185020
  10. [10] W. Ichinose, Remarks on Self-Adjointness of Operators in Quantum Mechanics and h-dependency of Solutions for Their Cauchy Problem, Preprint. 
  11. [11] H. Kumano-Go, Pseudo-Differential Operators, M.I.T. Press, Cambridge, 1981. 
  12. [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. Zbl0669.35115MR966395
  13. [13] M. Reed and B. Simon, Methods of Modern Mathematical Physics II, Fourier Analysis, Self-Adjointness, Academic Press, New York and London, 1975. Zbl0308.47002MR493420
  14. [14] M. Reed and B. Simon, Methods of Modern Mathematical Physics IV, Analysis of Operators, Academic Press, New York and London, 1978. Zbl0401.47001MR493421
  15. [15] M.A. Shubin, Pseudodifferential Operators and Spectral Theory, Springer-Verlag, Berlin and Heidelberg, 1987. Zbl0616.47040MR883081
  16. [16] R.A. Weder, Spectral Analysis of Pseudodifferential Operators, J. Functional Anal., Vol. 20, 1975, pp. 319-337. Zbl0317.47035MR402547

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