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  • 1
    Digitale Medien
    Digitale Medien
    Hypervirial theorem and parameter differentiation: Closed formulation for harmonic oscillator integrals (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 1032-1035 
    Details
    ISSN: 1089-7658
    Quelle: AIP Digital Archive
    Thema: Mathematik , Physik
    Notizen: A simple method has been developed to generate a closed formula for the calculation of matrix elements of arbitrary functions f(x) in the representation of the harmonic oscillator. The proposed algebraic procedure is based on the combined use of the hypervirial theorem with and without the second quantization formalism along with the parameter differentiation technique. The closed formula thus obtained is given in terms of a sum involving the jth derivative of f(x) evaluated at zero.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.527543
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  • 2
    Digitale Medien
    Digitale Medien
    Two-center integrals for arbitrary potentials: franck-condon factors
    Amsterdam : Elsevier
    Chemical Physics Letters 135 (1987), S. 149-152 
    Details
    ISSN: 0009-2614
    Quelle: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Thema: Chemie und Pharmazie , Physik
    Materialart: Digitale Medien
    URL: http://linkinghub.elsevier.com/retrieve/pii/0009-2614(87)87234-2
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  • 3
    Digitale Medien
    Digitale Medien
    A Generator for the Weert Superpotential (1999)
    Springer
    International journal of theoretical physics 38 (1999), S. 939-943 
    Details
    ISSN: 1572-9575
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract Weert found a superpotential $$\mathop {K_{ijc} }\limits_{\text{B}}$$ for the bounded part of the Maxwelltensor $$\mathop {T_{ijc} }\limits_{\text{B}}$$ associatedto the Lienard–Wiechert field. Here we obtain afourth-rank generator $$\mathop {K_{abcr} }\limits_{\text{B}}$$ for the superpotential $$\mathop {K_{abc} }\limits_{\text{B}}$$ .
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1026625506601
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  • 4
    Digitale Medien
    Digitale Medien
    Letter: Lanczos Spintensor for the Godel Metric (1999)
    Springer
    General relativity and gravitation 31 (1999), S. 1071-1074 
    Details
    ISSN: 1572-9532
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract A Lanczos potential in Godel geometry is obtained.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1026739800358
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  • 5
    Digitale Medien
    Digitale Medien
    Letter: A Potential for the Lanczos Spintensor in Kerr Geometry (1999)
    Springer
    General relativity and gravitation 31 (1999), S. 413-415 
    Details
    ISSN: 1572-9532
    Schlagwort(e): LANCZOS SUPERPOTENTIAL ; LANCZOS GENERATOR FOR THE WEYL TENSOR ; HIERARCHY OF POTENTIALS FOR THE CONFORMALTENSOR
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We show a generator of the Lanczos spintensorfor a rotating black hole.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1026653030033
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  • 6
    Digitale Medien
    Digitale Medien
    Letter: A Potential for the Radiative Part of the Lienard Wiechert Field (1999)
    Springer
    General relativity and gravitation 31 (1999), S. 1931-1934 
    Details
    ISSN: 1572-9532
    Schlagwort(e): NON-LOCAL POTENTIAL FOR THE ELECTROMAGNETICFIELD ; LANCZOS GENERATOR
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We show a superpotential totally non-local whichgenerates the radiative part of the Maxwell tensor ofLienard-Wiechert.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1026795023924
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  • 7
    Digitale Medien
    Digitale Medien
    Ladder operators for central potential wave functions from the algebraic representation of orthogonal polynomials (1991)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 40 (1991), S. 155-164 
    Details
    ISSN: 0020-7608
    Schlagwort(e): Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie
    Notizen: A general algebraic procedure that yields to raising and lowering operators for the solutions of second-order differential equations is presented. The method is illustrated by applying it to the differential equations of Hermite and Laguerre polynomials. Taking advantage of the algebraic representation of these polynomials, the ladder operators for harmonic oscillator and hydrogen atom wavefunctions are straightforwardly deduced without resorting to specialized factorizations. The proposed algebraic approach can be extended to the determination of new sets of ladder operators that could be used in the calculation of matrix elements in specific applications.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/qua.560400818
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  • 8
    Digitale Medien
    Digitale Medien
    Alternative approach to the factorization method (1992)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 44 (1992), S. 171-179 
    Details
    ISSN: 0020-7608
    Schlagwort(e): Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie
    Notizen: A procedure to obtain the operational solutions of second order differential equations related with Sturm-Liouville problems is presented. The method is based on the commutation relation between the ladder operators themselves, with a certain structure, and the position and momentum operators. Even though the creation and annihilation operators, derived by the proposed approach, factorize as expected the corresponding differential equation, the method does not use, as original premise factoring, the differential relation under consideration. That is, the displayed procedure is quite different, simple, and direct when compared with other procedures such as the factorization method of Infeld and Hull. To illustrate the above, the usefulness of the proposed procedure is shown by finding the ladder operators associated to the quantum numbers n and I for various potential wave functions. © 1992 John Wiley & Sons, Inc.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/qua.560440816
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  • 9
    Digitale Medien
    Digitale Medien
    Improved recursion formulas for the calculation of two-center central potential integrals (1995)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 56 (1995), S. 339-347 
    Details
    ISSN: 0020-7608
    Schlagwort(e): Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie
    Notizen: A commutator algebra procedure is used to get improved recurrence relations for the calculation of any f(r) off-diagonal two-center matrix elements in the general case of displaced arbitrary central potential wave functions. As expected, the proposed formulas reduce properly to the generalized recursion equations for the calculation of one-center integrals. Besides, when f(r) = rk, one obtains the equivalent of the Kramer rule for two-center multipolar matrix elements for arbitrary potentials, and when f(r) is constant, the Wu formula (for the calculation of Franck-Condon factors) is ameliorated in the sense that the new relation not necessarily considers equal mass. Furthermore, all diagonal matrix elements as well as all off-diagonal integrals between nondisplaced potentials appear, in our treatment, as particular cases in good agreement with already published results. As a useful application, the corresponding recurrence relations for the calculation of one-center hydrogenic matrix elements and two-center Kratzer potential integrals are given as examples. However, our approach is general and can be easily extended to obtain recursion formulae for other potential wave functions. © 1995 John Wiley & Sons, Inc.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/qua.560560838
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  • 10
    Digitale Medien
    Digitale Medien
    Oscillators in one and two dimensions and ladder operators for the Morse and Coulomb problems (1997)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 177-183 
    Details
    ISSN: 0020-7608
    Schlagwort(e): Chemistry ; Theoretical, Physical and Computational Chemistry
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie
    Notizen: We exhibit that the radial eigenfunctions of a 2D-harmonic oscillator (2DHO) may be regarded as 1D-harmonic oscillator (1DHO) matrix elements. From this simple fact and using as a starting point the ladder operators â± for 1DHO, we obtain ladder operators for 2DHO. Furthermore, by using the relationship between the Coulomb and Morse problems with a 2DHO, we are able to obtain the ladder operators for the former problems without explicitly recurring to the factorization method. Some uses of the technique presented are suggested. © 1997 John Wiley & Sons, Inc.
    Materialart: Digitale Medien
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