메뉴 건너뛰기




Volumn 39, Issue 5, 1998, Pages 2551-2563

An exactly soluble Schrödinger equation with smooth position-dependent mass

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0032371665     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532407     Document Type: Article
Times cited : (174)

References (40)
  • 1
    • 0346895729 scopus 로고
    • Resonant level lifetime in the double barrier structure for both quasi-bound and extended states
    • J.-P. Peng, Y.-M. Mu, and X.-C. Shen, "Resonant level lifetime in the double barrier structure for both quasi-bound and extended states," J. Appl. Phys. 73, 989-991 (1993).
    • (1993) J. Appl. Phys. , vol.73 , pp. 989-991
    • Peng, J.-P.1    Mu, Y.-M.2    Shen, X.-C.3
  • 2
    • 0026943882 scopus 로고
    • Density-of-states formalism for multi-quantum-barrier structures
    • R. Kucharczyk and M. Stȩslicka, "Density-of-states formalism for multi-quantum-barrier structures," Solid State Commun. 84, 727-730 (1992).
    • (1992) Solid State Commun. , vol.84 , pp. 727-730
    • Kucharczyk, R.1    Stȩslicka, M.2
  • 3
    • 0027543213 scopus 로고
    • Transmission coefficient and Stark shifts in double-barrier quantum well structures
    • F. Berz, "Transmission coefficient and Stark shifts in double-barrier quantum well structures," Semicond. Sci. Technol. 8, 243-253 (1993).
    • (1993) Semicond. Sci. Technol. , vol.8 , pp. 243-253
    • Berz, F.1
  • 4
    • 0347526498 scopus 로고
    • Local density of states in double-barrier resonant-tunneling structures. II. Finite-width barriers
    • J. D. Bruno and T. B. Bahder, "Local density of states in double-barrier resonant-tunneling structures. II. Finite-width barriers," Phys. Rev. B 39, 3659-3663 (1989).
    • (1989) Phys. Rev. B , vol.39 , pp. 3659-3663
    • Bruno, J.D.1    Bahder, T.B.2
  • 6
    • 0000438387 scopus 로고
    • Interface connection rules for effective-mass wave functions at an abrupt heterojunction between two different semi-conductors
    • Qi-G. Zhu and H. Kroemer, "Interface connection rules for effective-mass wave functions at an abrupt heterojunction between two different semi-conductors," Phys. Rev. B 27, 3519-3527 (1983).
    • (1983) Phys. Rev. B , vol.27 , pp. 3519-3527
    • Zhu, Q.-G.1    Kroemer, H.2
  • 7
    • 20444439923 scopus 로고
    • Space-charge effects on electron tunneling
    • D. J. Ben Daniel and C. B. Duke, "Space-charge effects on electron tunneling," Phys. Rev. 152, 683-692 (1966).
    • (1966) Phys. Rev. , vol.152 , pp. 683-692
    • Ben Daniel, D.J.1    Duke, C.B.2
  • 9
    • 0005064527 scopus 로고
    • Operator ordering in effective-mass theory
    • J. Thomsen, G. T. Einevoll, and P. C. Hemmer, "Operator ordering in effective-mass theory," Phys. Rev. B 39, 12 783-12 788 (1989).
    • (1989) Phys. Rev. B , vol.39 , pp. 12783-12788
    • Thomsen, J.1    Einevoll, G.T.2    Hemmer, P.C.3
  • 10
    • 0000639159 scopus 로고
    • Model effective-mass Hamiltonians for abrupt heterojunctions and the associated wave-function-matching conditions
    • R. A. Morrow and K. R. Brownstein, "Model effective-mass Hamiltonians for abrupt heterojunctions and the associated wave-function-matching conditions," Phys. Rev. B 30, 678-680 (1984).
    • (1984) Phys. Rev. B , vol.30 , pp. 678-680
    • Morrow, R.A.1    Brownstein, K.R.2
  • 11
    • 0001280866 scopus 로고
    • Establishment of an effective-mass Hamiltonian for abrupt heterojunctions
    • R. A. Morrow, "Establishment of an effective-mass Hamiltonian for abrupt heterojunctions," Phys. Rev. B 35, 8074-8079 (1987).
    • (1987) Phys. Rev. B , vol.35 , pp. 8074-8079
    • Morrow, R.A.1
  • 12
    • 4243742331 scopus 로고
    • Effective-mass Hamiltonians for abrupt heterojunctions in three dimensions
    • R. A. Morrow, "Effective-mass Hamiltonians for abrupt heterojunctions in three dimensions," Phys. Rev. B 36, 4836-4840 (1987).
    • (1987) Phys. Rev. B , vol.36 , pp. 4836-4840
    • Morrow, R.A.1
  • 13
    • 35949010876 scopus 로고
    • Operator ordering in effective-mass theory for heterostructures. II. Strained systems
    • G. T. Einvoll, "Operator ordering in effective-mass theory for heterostructures. II. Strained systems," Phys. Rev. B 42, 3497-3502 (1990).
    • (1990) Phys. Rev. B , vol.42 , pp. 3497-3502
    • Einvoll, G.T.1
  • 14
    • 0000867614 scopus 로고
    • Position-dependent effective mass for inhomogeneous semiconductors
    • K. Young, "Position-dependent effective mass for inhomogeneous semiconductors," Phys. Rev. B 39, 13 434-13 441 (1989).
    • (1989) Phys. Rev. B , vol.39 , pp. 13434-13441
    • Young, K.1
  • 15
    • 31144441358 scopus 로고
    • The effective-mass Hamiltonian for abrupt heterostructures
    • G. T. Einevoll and P. C. Hemmer, "The effective-mass Hamiltonian for abrupt heterostructures," J. Phys. C 21, L1193-L1198 (1988).
    • (1988) J. Phys. C , vol.21
    • Einevoll, G.T.1    Hemmer, P.C.2
  • 16
    • 24244454872 scopus 로고
    • Position-dependent effective masses in semiconductor theory
    • O. Von Roos, "Position-dependent effective masses in semiconductor theory," Phys. Rev. B 27, 7547-7552 (1983).
    • (1983) Phys. Rev. B , vol.27 , pp. 7547-7552
    • Von Roos, O.1
  • 17
    • 0012143869 scopus 로고
    • Boundary conditions and interface states in heterostructures
    • W. Trzeciakowski, "Boundary conditions and interface states in heterostructures," Phys. Rev. B 38, 4322-4325 (1988).
    • (1988) Phys. Rev. B , vol.38 , pp. 4322-4325
    • Trzeciakowski, W.1
  • 18
    • 0000756123 scopus 로고
    • Envelope-function matching conditions for GaAs/(Al, Ga)As heterojunctions
    • I. Galbraith and G. Duggan, "Envelope-function matching conditions for GaAs/(Al, Ga)As heterojunctions," Phys. Rev. B 38, 10 057-10 059 (1988).
    • (1988) Phys. Rev. B , vol.38 , pp. 10057-10059
    • Galbraith, I.1    Duggan, G.2
  • 19
    • 36049058438 scopus 로고
    • Theory of electronic states and transport in graded mixed semiconductors
    • T. Gora and F. Williams, "Theory of electronic states and transport in graded mixed semiconductors," Phys. Rev. 177, 1179-1182 (1969).
    • (1969) Phys. Rev. , vol.177 , pp. 1179-1182
    • Gora, T.1    Williams, F.2
  • 20
    • 24244478472 scopus 로고
    • Position-dependent effective masses in semiconductor theory. II
    • O. Von Roos and H. Mavromatis, "Position-dependent effective masses in semiconductor theory. II," Phys. Rev. B 31, 2294-2298 (1985).
    • (1985) Phys. Rev. B , vol.31 , pp. 2294-2298
    • Von Roos, O.1    Mavromatis, H.2
  • 21
    • 35949014926 scopus 로고
    • Operator ordering in effective-mass theory for heterostructures. I. Comparison with exact results for superlattices, quantum wells, and localized potentials
    • G. T. Einevoll, P. C. Hemmer, and J. Thomsen, "Operator ordering in effective-mass theory for heterostructures. I. Comparison with exact results for superlattices, quantum wells, and localized potentials," Phys. Rev. B 42, 3485-3496 (1990).
    • (1990) Phys. Rev. B , vol.42 , pp. 3485-3496
    • Einevoll, G.T.1    Hemmer, P.C.2    Thomsen, J.3
  • 22
    • 33750906134 scopus 로고
    • Position-dependent effective mass and Galilean invariance
    • J.-M. Lévy-Leblond, "Position-dependent effective mass and Galilean invariance," Phys. Rev. A 52, 1845-1849 (1995).
    • (1995) Phys. Rev. A , vol.52 , pp. 1845-1849
    • Lévy-Leblond, J.-M.1
  • 23
    • 35949024093 scopus 로고
    • Superlattice band structure in the envelope-function approximation
    • G. Bastard, "Superlattice band structure in the envelope-function approximation," Phys. Rev. B 24, 5693-5697 (1981).
    • (1981) Phys. Rev. B , vol.24 , pp. 5693-5697
    • Bastard, G.1
  • 24
    • 0002033457 scopus 로고
    • Green's functions via path integrals for systems with position-dependent masses
    • L. Chetouani, L. Dekar, and T. F. Hammann, "Green's functions via path integrals for systems with position-dependent masses," Phys. Rev. A 52, 82-91 (1995).
    • (1995) Phys. Rev. A , vol.52 , pp. 82-91
    • Chetouani, L.1    Dekar, L.2    Hammann, T.F.3
  • 25
    • 0037977326 scopus 로고
    • Elementary quantum models with position-dependent mass
    • J.-M. Lévy-Leblond, "Elementary quantum models with position-dependent mass," Eur. J. Phys. 13, 215-218 (1992).
    • (1992) Eur. J. Phys. , vol.13 , pp. 215-218
    • Lévy-Leblond, J.-M.1
  • 26
    • 34447590685 scopus 로고
    • Zur Theorie der Riemann'schen Functionen zweiter Ordnung mit vier Verweigungspunkten
    • K. Heun, "Zur Theorie der Riemann'schen Functionen zweiter Ordnung mit vier Verweigungspunkten," Math. Ann. 33, 161-179 (1889).
    • (1889) Math. Ann. , vol.33 , pp. 161-179
    • Heun, K.1
  • 27
    • 0346265378 scopus 로고
    • Beiträge zur Theorie der Lamé'schen Functionen
    • K. Heun, "Beiträge zur Theorie der Lamé'schen Functionen," Math. Ann. 33, 180-196 (1889).
    • (1889) Math. Ann. , vol.33 , pp. 180-196
    • Heun, K.1
  • 28
    • 0010863967 scopus 로고
    • Hypergeometric and Legendre Functions with Applications to Integral Equations of Potential Theory
    • Chap. VII
    • C. Snow, Hypergeometric and Legendre Functions With Applications to Integral Equations of Potential Theory, National Bureau of Standards Applied Mathematics Series, 1952, Vol. 19, Chap. VII, p. 87-101.
    • (1952) National Bureau of Standards Applied Mathematics Series , vol.19 , pp. 87-101
    • Snow, C.1
  • 30
    • 84972500553 scopus 로고
    • The Fuchsian equation of second order with four singularities
    • A. Erdélyi, "The Fuchsian equation of second order with four singularities," Duke Math. J. 9, 48-58 (1942).
    • (1942) Duke Math. J. , vol.9 , pp. 48-58
    • Erdélyi, A.1
  • 31
    • 0012070643 scopus 로고
    • Certain expansions of solutions of the Heun equation
    • A. Erdélyi, "Certain expansions of solutions of the Heun equation," Q. J. Math. Oxford Ser. 15, 62-69 (1944).
    • (1944) Q. J. Math. Oxford Ser. , vol.15 , pp. 62-69
    • Erdélyi, A.1
  • 34
    • 85033919033 scopus 로고    scopus 로고
    • Reference 28, p. 89, Eqs. (6a), (7), and (7′)
    • Reference 28, p. 89, Eqs. (6a), (7), and (7′).
  • 35
    • 85033905170 scopus 로고    scopus 로고
    • Reference 28, p. 91, Eq. (9b)
    • Reference 28, p. 91, Eq. (9b).
  • 36
    • 85033935536 scopus 로고    scopus 로고
    • Reference 28, p. 88, Eq. (3)
    • Reference 28, p. 88, Eq. (3).
  • 37
    • 85033933749 scopus 로고    scopus 로고
    • Reference 28, p. 98, Eqs. (20a) and (20b)
    • Reference 28, p. 98, Eqs. (20a) and (20b).
  • 38
    • 85033937256 scopus 로고    scopus 로고
    • Reference 28, p. 95, Eq. (16a)
    • Reference 28, p. 95, Eq. (16a).
  • 39
    • 85033913913 scopus 로고    scopus 로고
    • Reference 26, Sec. 4, pp. 173-179
    • Reference 26, Sec. 4, pp. 173-179.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.