메뉴 건너뛰기




Volumn 2000, Issue , 2010, Pages 1-188

Regularity and approximability of electronic wave functions

Author keywords

[No Author keywords available]

Indexed keywords


EID: 77952922742     PISSN: 00758434     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-642-12248-4_1     Document Type: Article
Times cited : (67)

References (100)
  • 4
    • 0342843084 scopus 로고
    • Asymptotic behavior of atomic bound state wavefunctions
    • Ahlrichs, R.: Asymptotic behavior of atomic bound state wavefunctions. J. Math. Phys. 14, 1860-1863 (1973)
    • (1973) J. Math. Phys. , vol.14 , pp. 1860-1863
    • Ahlrichs, R.1
  • 5
    • 65549134850 scopus 로고    scopus 로고
    • Springer, Berlin Heidelberg New York
    • Aigner, M.: A Course in Enumeration. Springer, Berlin Heidelberg New York (2007)
    • (2007) A Course in Enumeration
    • Aigner, M.1
  • 7
    • 0000330481 scopus 로고
    • Approximation by trigonometric polynomials in a certain class of periodic functions of several variables
    • Babenko, K.: Approximation by trigonometric polynomials in a certain class of periodic functions of several variables. Sov. Math., Dokl. 1, 672-675 (1960)
    • (1960) Sov. Math., Dokl. , vol.1 , pp. 672-675
    • Babenko, K.1
  • 8
    • 84966243578 scopus 로고
    • Finite element-Galerkin approximation of the eigenvalues and eigenvectors of selfadjoint problems
    • Babuška, I., Osborn, J.: Finite element-Galerkin approximation of the eigenvalues and eigenvectors of selfadjoint problems. Math. Comput. 52, 275-297 (1989)
    • (1989) Math. Comput. , vol.52 , pp. 275-297
    • Babuška, I.1    Osborn, J.2
  • 9
    • 54249116319 scopus 로고
    • Eigenvalue problems
    • P. Ciarlet, J. Lions (eds.) Finite Element Methods (Part 1), Elsevier, Amsterdam
    • Babuška, I., Osborn, J.: Eigenvalue problems. In: P. Ciarlet, J. Lions (eds.) Handbook of Numerical Analysis, Vol.II, Finite Element Methods (Part 1), pp. 641-792. Elsevier, Amsterdam (1991)
    • (1991) Handbook of Numerical Analysis , vol.2 , pp. 641-792
    • Babuška, I.1    Osborn, J.2
  • 10
    • 41549103799 scopus 로고    scopus 로고
    • Approximating a wavefunction as an unconstrained sum of Slater determinants
    • 107
    • Beylkin, G., Mohlenkamp, M., Perez, F.: Approximating a wavefunction as an unconstrained sum of Slater determinants. J. Math. Phys. 49, 032,107 (2008)
    • (2008) J. Math. Phys. , vol.49 , pp. 032
    • Beylkin, G.1    Mohlenkamp, M.2    Perez, F.3
  • 11
    • 84973654655 scopus 로고
    • Zur Quantentheorie der Molekeln
    • Born, M., Oppenheimer, R.: Zur Quantentheorie der Molekeln. Ann. der Physik 84, 457-484 (1927)
    • (1927) Ann. der Physik , vol.84 , pp. 457-484
    • Born, M.1    Oppenheimer, R.2
  • 12
    • 0000567090 scopus 로고
    • A general method of calculation for the stationary states of any molecular system
    • Boys, S.: A general method of calculation for the stationary states of any molecular system. Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 200, 542-554 (1950)
    • (1950) Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. , vol.200 , pp. 542-554
    • Boys, S.1
  • 13
    • 24344506306 scopus 로고
    • Asymptotics for the approximation of wave functions by exponential sums
    • Braess, D.: Asymptotics for the approximation of wave functions by exponential sums. J. Approx. Theory 83, 93-103 (1995)
    • (1995) J. Approx. Theory , vol.83 , pp. 93-103
    • Braess, D.1
  • 14
    • 0036003401 scopus 로고    scopus 로고
    • On the stability of the L2-projection in H1(ω)
    • Bramble, J., Pasciak, J., Steinbach, O.: On the stability of the L2-projection in H1(ω). Math. Comput. 71, 147-156 (2001)
    • (2001) Math. Comput. , vol.71 , pp. 147-156
    • Bramble, J.1    Pasciak, J.2    Steinbach, O.3
  • 17
    • 0036003405 scopus 로고    scopus 로고
    • Merging the Bramble-Pasciak-Steinbach and the Crouzeix-Thoḿee criterion for H1-stability of the L2-projection onto finite element spaces
    • Carstensen, C.: Merging the Bramble-Pasciak-Steinbach and the Crouzeix-Thoḿee criterion for H1-stability of the L2-projection onto finite element spaces. Math. Comput. 71, 157-163 (2001)
    • (2001) Math. Comput. , vol.71 , pp. 157-163
    • Carstensen, C.1
  • 19
    • 33847654434 scopus 로고
    • Asymptotic behavior of eigenfunctions for multiparticle Schrödinger operators
    • Combes, J., Thomas, L.: Asymptotic behavior of eigenfunctions for multiparticle Schrödinger operators. Commun. Math. Phys. 34, 251-270 (1973)
    • (1973) Commun. Math. Phys. , vol.34 , pp. 251-270
    • Combes, J.1    Thomas, L.2
  • 20
    • 33947217211 scopus 로고
    • Exponential decay of bound state wave functions
    • Connor, A.O.: Exponential decay of bound state wave functions. Commun. Math. Phys. 32, 319-340 (1973)
    • (1973) Commun. Math. Phys. , vol.32 , pp. 319-340
    • Connor, A.O.1
  • 22
    • 34250284345 scopus 로고
    • Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems IV
    • Deift, P., Hunziker, W., Simon, B., Vock, E.: Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems IV. Commun. Math. Phys. 64, 1-34 (1978)
    • (1978) Commun. Math. Phys. , vol.64 , pp. 1-34
    • Deift, P.1    Hunziker, W.2    Simon, B.3    Vock, E.4
  • 23
    • 0003017186 scopus 로고
    • D-variate Boolean interpolation
    • Delvos, F.: d-variate Boolean interpolation. J. Approx. Theory 34, 99-114 (1982)
    • (1982) J. Approx. Theory , vol.34 , pp. 99-114
    • Delvos, F.1
  • 24
    • 0003199283 scopus 로고
    • Boolean methods in Interpolation and Approximation
    • John Wiley & Sons, New York
    • Delvos, F., Schempp, W.: Boolean methods in Interpolation and Approximation. Pitman Research Notes in Mathematics, vol.230. John Wiley & Sons, New York (1989)
    • (1989) Pitman Research Notes in Mathematics , vol.230
    • Delvos, F.1    Schempp, W.2
  • 29
    • 0037158540 scopus 로고    scopus 로고
    • Wavelet approximation of correlated wave functions. II. Hyperbolic wavelets and adaptive approximation schemes
    • Flad, H.J., Hackbusch, W., Kolb, D., Koprucki, T.: Wavelet approximation of correlated wave functions. II. Hyperbolic wavelets and adaptive approximation schemes. J. Chem. Phys. 117, 3625-3638 (2002)
    • (2002) J. Chem. Phys. , vol.117 , pp. 3625-3638
    • Flad, H.J.1    Hackbusch, W.2    Kolb, D.3    Koprucki, T.4
  • 30
    • 33646684529 scopus 로고    scopus 로고
    • Best N-term approximation in electronic structure calculations I. One-electron reduced density matrix
    • Flad, H.J., Hackbusch, W., Schneider, R.: Best N-term approximation in electronic structure calculations. I. One-electron reduced density matrix. M2AN 40, 49-61 (2006)
    • (2006) M2AN , vol.40 , pp. 49-61
    • Flad, H.J.1    Hackbusch, W.2    Schneider, R.3
  • 31
    • 34547512331 scopus 로고    scopus 로고
    • Best N-term approximation in electronic structure calculations. II. Jastrow factors
    • Flad, H.J., Hackbusch, W., Schneider, R.: Best N-term approximation in electronic structure calculations. II. Jastrow factors. M2AN 41, 261-279 (2007)
    • (2007) M2AN , vol.41 , pp. 261-279
    • Flad, H.J.1    Hackbusch, W.2    Schneider, R.3
  • 32
    • 56749170131 scopus 로고    scopus 로고
    • Asymptotic regularity of solutions of Hartree-Fock equations with Coulomb potential
    • Flad, H.J., Schneider, R., Schulze, B.W.: Asymptotic regularity of solutions of Hartree-Fock equations with Coulomb potential. Math. Methods Appl. Sci. 31, 2172-2201 (2008)
    • (2008) Math. Methods Appl. Sci. , vol.31 , pp. 2172-2201
    • Flad, H.J.1    Schneider, R.2    Schulze, B.W.3
  • 34
    • 0042977329 scopus 로고    scopus 로고
    • The multiconfiguration equations for atoms and molecules: Charge quantization and existence of solutions
    • Friesecke, G.: The multiconfiguration equations for atoms and molecules: charge quantization and existence of solutions. Arch. Ration. Mech. Anal. 169, 35-71 (2003)
    • (2003) Arch. Ration. Mech. Anal. , vol.169 , pp. 35-71
    • Friesecke, G.1
  • 35
    • 0001032475 scopus 로고    scopus 로고
    • On the computation of the eigenproblems of hydrogen and helium in strong magnetic and electric fields with the sparse grid combination technique
    • Garcke, J., Griebel, M.: On the computation of the eigenproblems of hydrogen and helium in strong magnetic and electric fields with the sparse grid combination technique. J. Comput. Phys. 165, 694-716 (2000)
    • (2000) J. Comput. Phys. , vol.165 , pp. 694-716
    • Garcke, J.1    Griebel, M.2
  • 36
    • 49949112371 scopus 로고    scopus 로고
    • Sparse grids and related approximation schemes for higher dimensional problems
    • Cambridge University Press, Cambridge
    • Griebel,M.: Sparse grids and related approximation schemes for higher dimensional problems. In: Foundations of Computational Mathematics, Santander 2005, Lond. Math. Soc. Lect. Note Ser., vol.331, pp. 106-161. Cambridge University Press, Cambridge (2006)
    • (2006) Foundations of Computational Mathematics, Santander 2005, Lond. Math. Soc. Lect. Note Ser. , vol.331 , pp. 106-161
    • Griebel, M.1
  • 37
    • 84878076169 scopus 로고    scopus 로고
    • A wavelet based sparse grid method for the electronic Schrödinger equation
    • Eur. Math. Soc., Zürich
    • Griebel, M., Hamaekers, J.: A wavelet based sparse grid method for the electronic Schrödinger equation. In: International Congress of Mathematicians, vol.III, pp. 1473-1506. Eur. Math. Soc., Zürich (2006)
    • (2006) International Congress of Mathematicians , vol.3 , pp. 1473-1506
    • Griebel, M.1    Hamaekers, J.2
  • 38
    • 34547545863 scopus 로고    scopus 로고
    • Sparse grids for the Schrödinger equation
    • Griebel, M., Hamaekers, J.: Sparse grids for the Schrödinger equation. M2AN 41, 215-247 (2007)
    • (2007) M2AN , vol.41 , pp. 215-247
    • Griebel, M.1    Hamaekers, J.2
  • 40
    • 0034885786 scopus 로고    scopus 로고
    • The efficient computation of certain determinants arising in the treatment of Schrödinger's equation
    • Hackbusch, W.: The efficient computation of certain determinants arising in the treatment of Schrödinger's equation. Computing 67, 35-56 (2000)
    • (2000) Computing , vol.67 , pp. 35-56
    • Hackbusch, W.1
  • 42
    • 84960612244 scopus 로고
    • Asymptotic formulae in combinatory analysis
    • Hardy, G., Ramanujan, S.: Asymptotic formulae in combinatory analysis. Proc. Lond. Math. Soc. 17, 75-115 (1918)
    • (1918) Proc. Lond. Math. Soc. , vol.17 , pp. 75-115
    • Hardy, G.1    Ramanujan, S.2
  • 47
    • 0040676511 scopus 로고
    • On the spectra of Schrödinger multiparticle Hamiltonians
    • Hunziker, W.: On the spectra of Schrödinger multiparticle Hamiltonians. Helv. Phys. Acta 39, 451-462 (1966)
    • (1966) Helv. Phys. Acta , vol.39 , pp. 451-462
    • Hunziker, W.1
  • 48
    • 0034397412 scopus 로고    scopus 로고
    • The quantum N-body problem
    • Hunziker, W., Sigal, I.: The quantum N-body problem. J. Math. Phys. 41, 3448-3510 (2000)
    • (2000) J. Math. Phys. , vol.41 , pp. 3448-3510
    • Hunziker, W.1    Sigal, I.2
  • 49
    • 84966238625 scopus 로고
    • Fundamental properties of Hamiltonian operators of Schrödinger type
    • Kato, T.: Fundamental properties of Hamiltonian operators of Schrödinger type. Trans. Am. Math. Soc. 70, 195-221 (1951)
    • (1951) Trans. Am. Math. Soc. , vol.70 , pp. 195-221
    • Kato, T.1
  • 50
    • 84980086883 scopus 로고
    • On the eigenfunctions of many-particle systems in quantum mechanics
    • Kato, T.: On the eigenfunctions of many-particle systems in quantum mechanics. Commun. Pure Appl. Math. 10, 151-177 (1957)
    • (1957) Commun. Pure Appl. Math. , vol.10 , pp. 151-177
    • Kato, T.1
  • 51
    • 33845532360 scopus 로고    scopus 로고
    • New a priori FEM error estimates for eigenvalues
    • Knyazev, A., Osborn, J.: New a priori FEM error estimates for eigenvalues. SIAM J. Numer. Anal. 43, 2647-2667 (2006)
    • (2006) SIAM J. Numer. Anal. , vol.43 , pp. 2647-2667
    • Knyazev, A.1    Osborn, J.2
  • 52
    • 0033235339 scopus 로고    scopus 로고
    • Nobel lecture: Electronic structure of matter-wave functions and density functional
    • Kohn,W.: Nobel lecture: Electronic structure of matter-wave functions and density functionals. Rev. Mod. Phys. 71, 1253-1266 (1999)
    • (1999) Rev. Mod. Phys. , vol.71 , pp. 1253-1266
    • Kohn, W.1
  • 53
    • 70350640425 scopus 로고    scopus 로고
    • Springer, Berlin Heidelberg New York
    • Königsberger, K.: Analysis 1. Springer, Berlin Heidelberg New York (2004)
    • (2004) Analysis 1
    • Königsberger, K.1
  • 54
    • 0000678550 scopus 로고
    • Approximate calculation of repeated integrals by number-theoretical methods (Russian)
    • Korobov, N.: Approximate calculation of repeated integrals by number-theoretical methods (Russian). Dokl. Akad. Nauk. SSSR 115, 1062-1065 (1957)
    • (1957) Dokl. Akad. Nauk. SSSR , vol.115 , pp. 1062-1065
    • Korobov, N.1
  • 55
    • 0001347330 scopus 로고
    • Approximate calculation of repeated integrals (Russian)
    • Korobov, N.: Approximate calculation of repeated integrals (Russian). Dokl. Akad. Nauk. SSSR 124, 1207-1210 (1959)
    • (1959) Dokl. Akad. Nauk. SSSR , vol.124 , pp. 1207-1210
    • Korobov, N.1
  • 56
    • 84987143342 scopus 로고
    • Theory of the expansion of wave functions in a Gaussian basis
    • Kutzelnigg, W.: Theory of the expansion of wave functions in a Gaussian basis. International Journal of Quantum Chemistry 51, 447-463 (1994)
    • (1994) International Journal of Quantum Chemistry , vol.51 , pp. 447-463
    • Kutzelnigg, W.1
  • 57
    • 77952917664 scopus 로고    scopus 로고
    • Le Bris, C. (ed.) Computational Chemistry. North Holland, Amsterdam
    • Le Bris, C. (ed.): Handbook of Numerical Analysis, Vol.X: Computational Chemistry. North Holland, Amsterdam (2003)
    • (2003) Handbook of Numerical Analysis , vol.10
  • 58
    • 19844366465 scopus 로고    scopus 로고
    • Computational chemistry from the perspective of numerical analysis
    • Le Bris, C.: Computational chemistry from the perspective of numerical analysis. Acta Numerica 14, 363-444 (2005)
    • (2005) Acta Numerica , vol.14 , pp. 363-444
    • Le Bris, C.1
  • 59
    • 19844378167 scopus 로고    scopus 로고
    • From atoms to crystals: A mathematical journey
    • Le Bris, C., Lions, P.: From atoms to crystals: a mathematical journey. Bull. Am. Math. Soc., New Ser. 42, 291-363 (2005)
    • (2005) Bull. Am. Math. Soc., New Ser. , vol.42 , pp. 291-363
    • Le Bris, C.1    Lions, P.2
  • 60
    • 0742306186 scopus 로고    scopus 로고
    • Solutions of the multiconfiguration equations in quantum chemistry
    • Lewin, M.: Solutions of the multiconfiguration equations in quantum chemistry. Arch. Ration. Mech. Anal. 171, 83-114 (2004)
    • (2004) Arch. Ration. Mech. Anal. , vol.171 , pp. 83-114
    • Lewin, M.1
  • 61
    • 0000368619 scopus 로고
    • The Hartree-Fock theory for Coulomb systems
    • Lieb, E., Simon, B.: The Hartree-Fock theory for Coulomb systems. Commun. Math. Phys. 53, 185-194 (1977)
    • (1977) Commun. Math. Phys. , vol.53 , pp. 185-194
    • Lieb, E.1    Simon, B.2
  • 62
    • 33846040104 scopus 로고
    • The Thomas-Fermi theory of atoms, molecules, and solids
    • Lieb, E., Simon, B.: The Thomas-Fermi theory of atoms, molecules, and solids. Adv. Math. 23, 22-116 (1977)
    • (1977) Adv. Math. , vol.23 , pp. 22-116
    • Lieb, E.1    Simon, B.2
  • 63
    • 0001929193 scopus 로고
    • Solutions of Hartree-Fock equations for Coulomb systems
    • Lions, P.: Solutions of Hartree-Fock equations for Coulomb systems. Commun. Math. Phys. 109, 33-97 (1987)
    • (1987) Commun. Math. Phys. , vol.109 , pp. 33-97
    • Lions, P.1
  • 64
  • 66
    • 0000782328 scopus 로고
    • Bounds for the discrete part of the spectrum of a semi-bounded Schrödinger operator
    • Persson, A.: Bounds for the discrete part of the spectrum of a semi-bounded Schrödinger operator. Math. Scand. 8, 143-153 (1960)
    • (1960) Math. Scand. , vol.8 , pp. 143-153
    • Persson, A.1
  • 67
    • 0033235336 scopus 로고    scopus 로고
    • Nobel lecture: Quantum chemical models
    • Pople, J.: Nobel lecture: Quantum chemical models. Rev. Mod. Phys. 71, 1267-1274 (1999) (Pubitemid 129329209)
    • (1999) Reviews of Modern Physics , vol.71 , Issue.5 , pp. 1267-1274
    • Pople, J.A.1
  • 68
    • 84963069472 scopus 로고
    • On the partition function p(n)
    • Rademacher, H.: On the partition function p(n). Proc. Lond. Math. Soc. 43, 241-254 (1937)
    • (1937) Proc. Lond. Math. Soc. , vol.43 , pp. 241-254
    • Rademacher, H.1
  • 73
    • 71549133994 scopus 로고    scopus 로고
    • Analysis of the projected coupled cluster method in electronic structure calculation
    • Schneider, R.: Analysis of the projected coupled cluster method in electronic structure calculation. Numer. Math. 113, 433-471 (2009)
    • (2009) Numer. Math. , vol.113 , pp. 433-471
    • Schneider, R.1
  • 74
    • 84975485648 scopus 로고
    • Quantisierung als Eigenwertproblem
    • Schrödinger, E.: Quantisierung als Eigenwertproblem. Ann. der Physik 79, 361-376 (1926)
    • (1926) Ann. der Physik , vol.79 , pp. 361-376
    • Schrödinger, E.1
  • 75
    • 84967800149 scopus 로고
    • Pointwise bounds on eigenfunctions and wave packets in N-body quantum system i
    • Simon, B.: Pointwise bounds on eigenfunctions and wave packets in N-body quantum system I. Proc. Am. Math. Soc. 208, 317-329 (1975)
    • (1975) Proc. Am. Math. Soc. , vol.208 , pp. 317-329
    • Simon, B.1
  • 76
    • 0034400587 scopus 로고    scopus 로고
    • Schrödinger operators in the twentieth century
    • Simon, B.: Schrödinger operators in the twentieth century. J. Math. Phys. 41, 3523-3555 (2000)
    • (2000) J. Math. Phys. , vol.41 , pp. 3523-3555
    • Simon, B.1
  • 77
    • 0001048297 scopus 로고
    • Quadrature and interpolation formulas for tensor products of certain classes of functions
    • Smolyak, S.: Quadrature and interpolation formulas for tensor products of certain classes of functions. Dokl. Akad. Nauk SSSR 4, 240-243 (1963)
    • (1963) Dokl. Akad. Nauk SSSR , vol.4 , pp. 240-243
    • Smolyak, S.1
  • 82
    • 0003904565 scopus 로고
    • Oxford University Press, Oxford
    • Titchmarsh, E.: Eigenfunction Expansions, vols. I and II. Oxford University Press, Oxford (1953, 1958)
    • (1953) Eigenfunction Expansions , vol.1-2
    • Titchmarsh, E.1
  • 90
    • 0001117305 scopus 로고
    • Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen
    • Weyl, H.: Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen. Math. Ann. 71, 441-479 (1912)
    • (1912) Math. Ann. , vol.71 , pp. 441-479
    • Weyl, H.1
  • 93
    • 2942635358 scopus 로고    scopus 로고
    • On the regularity of the electronic Schrödinger equation in Hilbert spaces of mixed derivatives
    • Yserentant, H.: On the regularity of the electronic Schrödinger equation in Hilbert spaces of mixed derivatives. Numer. Math. 98, 731-759 (2004)
    • (2004) Numer. Math. , vol.98 , pp. 731-759
    • Yserentant, H.1
  • 94
    • 23944464925 scopus 로고    scopus 로고
    • Sparse grid spaces for the numerical solution of the electronic Schrödinger equation
    • Yserentant, H.: Sparse grid spaces for the numerical solution of the electronic Schrödinger equation. Numer. Math. 101, 381-389 (2005)
    • (2005) Numer. Math. , vol.101 , pp. 381-389
    • Yserentant, H.1
  • 95
    • 33846827026 scopus 로고    scopus 로고
    • The hyperbolic cross space approximation of electronic wavefunctions
    • Yserentant, H.: The hyperbolic cross space approximation of electronic wavefunctions. Numer. Math. 105, 659-690 (2007)
    • (2007) Numer. Math. , vol.105 , pp. 659-690
    • Yserentant, H.1
  • 99
    • 0002870854 scopus 로고
    • A study of the spectrum of the Schrödinger operator for a system of several particles (Russian)
    • Zhislin, G.: A study of the spectrum of the Schrödinger operator for a system of several particles (Russian). Tr. Mosk. Mat. O.-va 9, 81-120 (1960)
    • (1960) Tr. Mosk. Mat. O.-va , vol.9 , pp. 81-120
    • Zhislin, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.