메뉴 건너뛰기




Volumn 38, Issue 2, 1997, Pages 556-570

Relativistic point interaction with Coulomb potential in one dimension

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0031538892     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.531877     Document Type: Article
Times cited : (9)

References (55)
  • 1
    • 0001244693 scopus 로고
    • Quantum mechanics of electrons in crystal lattices
    • R. de L. Kronig and W. G. Penney, "Quantum mechanics of electrons in crystal lattices," Proc. R. Soc. London, Ser. A 130, 499-513 (1931).
    • (1931) Proc. R. Soc. London, Ser. A , vol.130 , pp. 499-513
    • Kronig, R.D.L.1    Penney, W.G.2
  • 3
    • 0004243866 scopus 로고
    • edited by E. Burstein and S. Lundkvist Plenum, New York
    • E. O. Kane, in Tunneling Phenomena in Solids, edited by E. Burstein and S. Lundkvist (Plenum, New York, 1969).
    • (1969) Tunneling Phenomena in Solids
    • Kane, E.O.1
  • 4
    • 0000059055 scopus 로고
    • Relativistic quarks in one-dimensional periodic structures
    • B. McKellar and G. J. Stephenson, "Relativistic quarks in one-dimensional periodic structures," Phys. Rev. C 35, 2262-2271 (1987).
    • (1987) Phys. Rev. C , vol.35 , pp. 2262-2271
    • McKellar, B.1    Stephenson, G.J.2
  • 5
    • 4243704845 scopus 로고
    • Bound states and confining properties of relativistic point interaction potentials
    • F. Dominguez-Adame and E. Marciá, "Bound states and confining properties of relativistic point interaction potentials," J. Phys. A 22, L419-L423 (1989).
    • (1989) J. Phys. A , vol.22
    • Dominguez-Adame, F.1    Marciá, E.2
  • 6
    • 0001992010 scopus 로고
    • Klein's paradox and the relativistic point interaction
    • P. Seba, "Klein's paradox and the relativistic point interaction," Lett. Math. Phys. 18, 77-86 (1989).
    • (1989) Lett. Math. Phys. , vol.18 , pp. 77-86
    • Seba, P.1
  • 7
    • 0000142699 scopus 로고
    • Klein paradox and the Dirac-Kronig-Penney model
    • B. H. J. McKellar and G. J. Stephenson, Jr., "Klein paradox and the Dirac-Kronig-Penney model," Phys. Rev. A 36, 2566-2569 (1987).
    • (1987) Phys. Rev. A , vol.36 , pp. 2566-2569
    • McKellar, B.H.J.1    Stephenson G.J., Jr.2
  • 8
    • 84983831788 scopus 로고
    • Relativistic generalization of the Saxon-Hutner theorem
    • K. V. Bhagwat and R. Subramanian, "Relativistic generalization of the Saxon-Hutner theorem," Phys. Stat. Sol. B 48, 399-406 (1971).
    • (1971) Phys. Stat. Sol. B , vol.48 , pp. 399-406
    • Bhagwat, K.V.1    Subramanian, R.2
  • 9
    • 84983864406 scopus 로고
    • Generalizations of the Saxon-Hutner theorem in the relativistic domain
    • I. M. Mladenov, "Generalizations of the Saxon-Hutner theorem in the relativistic domain," Phys. Stat. Sol. B 145, K115-K119 (1988).
    • (1988) Phys. Stat. Sol. B , vol.145
    • Mladenov, I.M.1
  • 10
    • 0014579787 scopus 로고
    • Relativistic theory of Thamm surface states
    • S. G. Davison and M. Stȩślicka, "Relativistic theory of Thamm surface states," J. Phys. C 2, 1802-1807 (1969).
    • (1969) J. Phys. C , vol.2 , pp. 1802-1807
    • Davison, S.G.1    Stȩślicka, M.2
  • 12
    • 0005713108 scopus 로고
    • Kronig-Penney models for surface states
    • M. Stȩślicka, "Kronig-Penney models for surface states," Progr. Surf. Sci. 5, 157-259 (1974).
    • (1974) Progr. Surf. Sci. , vol.5 , pp. 157-259
    • Stȩślicka, M.1
  • 13
    • 0019585409 scopus 로고
    • A relativistic treatment of field-sustained surface states
    • C. L. Roy and G. Roy, "A relativistic treatment of field-sustained surface states," Physica B 106, 257-267 (1981).
    • (1981) Physica B , vol.106 , pp. 257-267
    • Roy, C.L.1    Roy, G.2
  • 14
    • 0019624111 scopus 로고
    • Relativistic surface states in the presence of an impurity and a distortion at the surface
    • C. L. Roy and G. Roy, "Relativistic surface states in the presence of an impurity and a distortion at the surface," Physica B 111, 51-61 (1981).
    • (1981) Physica B , vol.111 , pp. 51-61
    • Roy, C.L.1    Roy, G.2
  • 15
    • 25744449203 scopus 로고
    • Relativistic surface states of a semi-infinite chain acted on by an electric field
    • Y. Shen, "Relativistic surface states of a semi-infinite chain acted on by an electric field," Surf. Sci. Lett. 108, L477-L485 (1981).
    • (1981) Surf. Sci. Lett. , vol.108
    • Shen, Y.1
  • 16
    • 0040208856 scopus 로고
    • Relativistic scattering states for a finite chain with δ-function potentials of arbitrary position and strength
    • G. Gumbs, "Relativistic scattering states for a finite chain with δ-function potentials of arbitrary position and strength," Phys. Rev. A 32, 1208-1210 (1985).
    • (1985) Phys. Rev. A , vol.32 , pp. 1208-1210
    • Gumbs, G.1
  • 17
  • 18
    • 84995188236 scopus 로고
    • Analytic solution of the Dirac equation for the Kronig-Penney potential
    • M. L. Glasser and S. G. Davison, "Analytic solution of the Dirac equation for the Kronig-Penney potential," Int. J. Quantum Chem. S 3, 867-877 (1970).
    • (1970) Int. J. Quantum Chem. S , vol.3 , pp. 867-877
    • Glasser, M.L.1    Davison, S.G.2
  • 19
    • 4243392540 scopus 로고
    • Boundary conditions for the relativistic Kronig-Penney model
    • S. G. Davison and M. Stȩślicka, "Boundary conditions for the relativistic Kronig-Penney model," Phys. Rev. B 1, 1858-1860 (1970).
    • (1970) Phys. Rev. B , vol.1 , pp. 1858-1860
    • Davison, S.G.1    Stȩślicka, M.2
  • 20
    • 0040803249 scopus 로고
    • The relativistic Kronig-Penney Hamiltonian
    • J. E. Avron and A. Grossmann, "The relativistic Kronig-Penney Hamiltonian," Phys. Lett. A 56, 55-57 (1976).
    • (1976) Phys. Lett. A , vol.56 , pp. 55-57
    • Avron, J.E.1    Grossmann, A.2
  • 21
    • 25744436845 scopus 로고
    • Relativistic and nonrelativistic Kronig-Penney models
    • F. Domínguez-Adame, "Relativistic and nonrelativistic Kronig-Penney models," Am. J. Phys. 55, 1003-1006 (1987).
    • (1987) Am. J. Phys. , vol.55 , pp. 1003-1006
    • Domínguez-Adame, F.1
  • 22
    • 4243481134 scopus 로고
    • A generalized Dirac-Kronig-Penney model
    • F. Domínguez-Adame, "A generalized Dirac-Kronig-Penney model," J. Phys. Condensed Matter 1, 109-112 (1989).
    • (1989) J. Phys. Condensed Matter , vol.1 , pp. 109-112
    • Domínguez-Adame, F.1
  • 23
    • 0016102816 scopus 로고
    • On the relativistic electronic states of a monatomic and a diatomic one-dimensional lattice
    • N. D. Sen Gupta, "On the relativistic electronic states of a monatomic and a diatomic one-dimensional lattice," Phys. Stat. Sol. B 65, 351-357 (1974).
    • (1974) Phys. Stat. Sol. B , vol.65 , pp. 351-357
    • Sen Gupta, N.D.1
  • 24
    • 0019637190 scopus 로고
    • Relativistic effect on a deformed semi-infinite cristalline surface
    • Y. Shen, "Relativistic effect on a deformed semi-infinite cristalline surface," Phys. Stat. Sol. B 108, 255-260 (1981).
    • (1981) Phys. Stat. Sol. B , vol.108 , pp. 255-260
    • Shen, Y.1
  • 25
    • 0039024869 scopus 로고
    • Transfer-matrix and dispersion relation for one-dimensional relativistic model diatomic crystal
    • M. Metodieva and V. Detcheva, "Transfer-matrix and dispersion relation for one-dimensional relativistic model diatomic crystal," Comptes Rendues de l'Academie Bulgare des Sciences 39, 35-37 (1986).
    • (1986) Comptes Rendues de l'Academie Bulgare des Sciences , vol.39 , pp. 35-37
    • Metodieva, M.1    Detcheva, V.2
  • 26
    • 84987058229 scopus 로고
    • Relativistic treatment of localized states. A review
    • S. G. Davison and M. Stȩślicka, "Relativistic treatment of localized states. A review," Int. J. Quantum Chem. 4, 445-453 (1971).
    • (1971) Int. J. Quantum Chem. , vol.4 , pp. 445-453
    • Davison, S.G.1    Stȩślicka, M.2
  • 27
    • 0001145281 scopus 로고
    • The relativistic Tamm model
    • K. V. Bhagwat and R. Subramanian, "The relativistic Tamm model," J. Phys. C 5, 798-806 (1972).
    • (1972) J. Phys. C , vol.5 , pp. 798-806
    • Bhagwat, K.V.1    Subramanian, R.2
  • 28
    • 0010871616 scopus 로고
    • Relativistic effects on impurity states
    • K. V. Bhagwat and R. Subramanian, "Relativistic effects on impurity states," Physica 62, 614-622 (1972).
    • (1972) Physica , vol.62 , pp. 614-622
    • Bhagwat, K.V.1    Subramanian, R.2
  • 29
    • 0039024870 scopus 로고
    • Relativistic effects in the R-matrix theory of tunneling
    • B. D. Kandilarov and V. Detcheva, "Relativistic effects in the R-matrix theory of tunneling," Physica 68, 579-586 (1973).
    • (1973) Physica , vol.68 , pp. 579-586
    • Kandilarov, B.D.1    Detcheva, V.2
  • 30
    • 0000924162 scopus 로고
    • Ambiguities with the relativistic δ-function potential
    • B. Sutherland and D. C. Mattis, "Ambiguities with the relativistic δ-function potential," Phys. Rev. A 24, 1194-1197 (1981).
    • (1981) Phys. Rev. A , vol.24 , pp. 1194-1197
    • Sutherland, B.1    Mattis, D.C.2
  • 31
    • 0021374639 scopus 로고
    • A study of relativistic interface states
    • C. L. Roy and G. Roy, "A study of relativistic interface states," Phys. Stat. Sol. B 121, 717-730 (1984).
    • (1984) Phys. Stat. Sol. B , vol.121 , pp. 717-730
    • Roy, C.L.1    Roy, G.2
  • 32
    • 0040208857 scopus 로고
    • Dirac equation approach to scattering from interface potential steps and existence of interface states
    • V. Detcheva, M. Metodieva, and B. D. Kandilarov, "Dirac equation approach to scattering from interface potential steps and existence of interface states," Helv. Phys. Acta 26, 2777-2780 (1985).
    • (1985) Helv. Phys. Acta , vol.26 , pp. 2777-2780
    • Detcheva, V.1    Metodieva, M.2    Kandilarov, B.D.3
  • 33
    • 0000713508 scopus 로고
    • New analytically solvable models of relativistic point interactions
    • F. Gesztesy and P. Šeba, "New analytically solvable models of relativistic point interactions," Lett. Math. Phys. 13, 345-358 (1987).
    • (1987) Lett. Math. Phys. , vol.13 , pp. 345-358
    • Gesztesy, F.1    Šeba, P.2
  • 34
    • 0001177246 scopus 로고
    • Quantization of fermions interacting with point-like external fields
    • P. Falkensteiner and H. Grosse, "Quantization of fermions interacting with point-like external fields," Lett. Math. Phys. 14, 139-148 (1987).
    • (1987) Lett. Math. Phys. , vol.14 , pp. 139-148
    • Falkensteiner, P.1    Grosse, H.2
  • 35
    • 4243453758 scopus 로고
    • On the absorption of eigenvalues by continuous spectrum in the one and three dimensional Dirac equation
    • P. Šeba, "On the absorption of eigenvalues by continuous spectrum in the one and three dimensional Dirac equation," Czech. J. Phys. B 38, 1078-1093 (1988).
    • (1988) Czech. J. Phys. B , vol.38 , pp. 1078-1093
    • Šeba, P.1
  • 36
    • 4243704845 scopus 로고
    • Bound states and confining properties of relativistic point interaction potentials
    • F. Domínguez-Adame, "Bound states and confining properties of relativistic point interaction potentials," J. Phys. A 22, L419-L423 (1989).
    • (1989) J. Phys. A , vol.22
    • Domínguez-Adame, F.1
  • 37
    • 0001424925 scopus 로고
    • Dirac Hamiltonian with Coulomb potential and spherically symmetric shell contact interaction
    • J. Dittrich, P. Exner, and P. Šeba, "Dirac Hamiltonian with Coulomb potential and spherically symmetric shell contact interaction," J. Math. Phys. 33, 2207-2214 (1992).
    • (1992) J. Math. Phys. , vol.33 , pp. 2207-2214
    • Dittrich, J.1    Exner, P.2    Šeba, P.3
  • 39
    • 21144467028 scopus 로고
    • Localized solutions of one-dimensional nonlinear Dirac equations with point interaction potentials
    • F. Domínguez-Adame, "Localized solutions of one-dimensional nonlinear Dirac equations with point interaction potentials," J. Phys. A 26, 3863-3868 (1993).
    • (1993) J. Phys. A , vol.26 , pp. 3863-3868
    • Domínguez-Adame, F.1
  • 40
    • 0000990551 scopus 로고
    • Boundary conditions across a δ-function potential in the one-dimensional Dirac equation
    • C. L. Roy, "Boundary conditions across a δ-function potential in the one-dimensional Dirac equation," Phys. Rev. A 47, 3417-3419 (1993).
    • (1993) Phys. Rev. A , vol.47 , pp. 3417-3419
    • Roy, C.L.1
  • 41
    • 84963044735 scopus 로고
    • On the unique self-adjoint extension of the Dirac operator and the existence of the Green matrix
    • W. D. Evans, "On the unique self-adjoint extension of the Dirac operator and the existence of the Green matrix," Proc. London Math. Soc. (3) 20, 537-557 (1970).
    • (1970) Proc. London Math. Soc. , vol.20 , Issue.3 , pp. 537-557
    • Evans, W.D.1
  • 42
    • 0040803257 scopus 로고
    • Distinguished selfadjoint extensions of Dirac operators
    • U.-W. Schmincke, "Distinguished selfadjoint extensions of Dirac operators," Math. Z. 129, 335-349 (1972).
    • (1972) Math. Z. , vol.129 , pp. 335-349
    • Schmincke, U.-W.1
  • 43
    • 4243427955 scopus 로고
    • Dirac operators with strongly singular potentials
    • R. Wüst, "Dirac operators with strongly singular potentials," Math. Z. 152, 259-271 (1977).
    • (1977) Math. Z. , vol.152 , pp. 259-271
    • Wüst, R.1
  • 44
    • 0001415359 scopus 로고
    • Remark on essential self-adjointness of Dirac operators with Coulomb potentials
    • V. Vogelsang, "Remark on essential self-adjointness of Dirac operators with Coulomb potentials," Math. Z. 196, 517-521 (1987).
    • (1987) Math. Z. , vol.196 , pp. 517-521
    • Vogelsang, V.1
  • 47
    • 0000895117 scopus 로고
    • Excitons and biexcitons in semiconductor quantum wires
    • L. Bányai, I. Galbraith, C. Ell, and H. Haug, "Excitons and biexcitons in semiconductor quantum wires," Phys. Rev. B 36, 6099-6104 (1987).
    • (1987) Phys. Rev. B , vol.36 , pp. 6099-6104
    • Bányai, L.1    Galbraith, I.2    Ell, C.3    Haug, H.4
  • 48
    • 0000715335 scopus 로고
    • Computation of tunneling rates in time-dependent electric fields: Electrons on the surface of liquid helium, a one-dimensional hydrogen atom
    • G. F. Saville and J. M. Goodkind, "Computation of tunneling rates in time-dependent electric fields: Electrons on the surface of liquid helium, a one-dimensional hydrogen atom," Phys. Rev. A 50, 2059-2067 (1994).
    • (1994) Phys. Rev. A , vol.50 , pp. 2059-2067
    • Saville, G.F.1    Goodkind, J.M.2
  • 49
    • 76549105667 scopus 로고
    • The theory of extensions and explicitly-soluble models
    • B. S. Pavlov, "The theory of extensions and explicitly-soluble models," Russian Math. Surveys 42:6, 127-168 (1987).
    • (1987) Russian Math. Surveys , vol.42 , Issue.6 , pp. 127-168
    • Pavlov, B.S.1
  • 51
    • 0039617101 scopus 로고
    • Self-adjoint extensions of Schroedinger operators with singular potentials
    • Birkhäuser, Basel
    • A. N. Kochubei, "Self-adjoint extensions of Schroedinger operators with singular potentials," in Operator Theory: Advances and Applications, Vol. 46 (Birkhäuser, Basel, 1990).
    • (1990) Operator Theory: Advances and Applications , vol.46
    • Kochubei, A.N.1
  • 53
    • 21844515931 scopus 로고
    • The functional-analytic versus the functional-integral approach to quantum Hamiltonians: The one-dimensional hydrogen atom
    • W. Fischer, H. Leschke, and P. Müller, "The functional-analytic versus the functional-integral approach to quantum Hamiltonians: The one-dimensional hydrogen atom," J. Math. Phys. 36, 2313-2323 (1995).
    • (1995) J. Math. Phys. , vol.36 , pp. 2313-2323
    • Fischer, W.1    Leschke, H.2    Müller, P.3
  • 54
    • 44949267668 scopus 로고
    • A new class of point interactions in one dimension
    • P. R. Chernoff and R. J. Hughes, "A new class of point interactions in one dimension," J. Funct. Anal. 111, 97-117 (1993).
    • (1993) J. Funct. Anal. , vol.111 , pp. 97-117
    • Chernoff, P.R.1    Hughes, R.J.2
  • 55
    • 0000128397 scopus 로고
    • Fundamental solution of the heat and Schrödinger equations with point interaction
    • S. Albeverio, Z. Brzeźniak, and L. Da̧browski, "Fundamental solution of the heat and Schrödinger equations with point interaction," J. Funct. Anal. 130, 220-254 (1995).
    • (1995) J. Funct. Anal. , vol.130 , pp. 220-254
    • Albeverio, S.1    Brzeźniak, Z.2    Da̧browski, L.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.