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  • 1
    Electronic Resource
    Electronic Resource
    A no-go theorem for a Lie-consistent q-Campbell–Baker–Hausdorff expansion (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6172-6178 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Lie consistency is defined for commutator expansions and it is shown that while a weakly Lie-consistent q-Campbell–Baker–Hausdorff expansion for a product of two M-type (but not P-type) q exponentials can be formulated, a strongly Lie-consistent expansion only exists for the undeformed case, q=1.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530736
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  • 2
    Electronic Resource
    Electronic Resource
    Nonspurious harmonic oscillator states in single particle coordinates (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1164-1166 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A procedure for the construction of nonspurious harmonic oscillator wave functions with arbitrary permutational symmetry has recently been proposed. The resulting wave functions are expressed in terms of normalized Jacobi coordinates, and involve a new type of harmonic oscillator coefficients of fractional parentage. A simple algorithm to transform these states from the Jacobi coordinates to the single particle coordinates is presented. This is a generalization to an arbitrary number of particles of the harmonic oscillator transformation from center-of-mass and relative coordinates to single particle coordinates.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528747
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  • 3
    Electronic Resource
    Electronic Resource
    The Korteweg–de Vries hierarchy of isospectral transformations: Towards a general explicit expression (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 1344-1350 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The structure of the Korteweg–de Vries hierarchy of evolution equations, generating isospectral transformations, is elucidated by means of a study of its recurrence relations. For the mth member of the KdV hierarchy, which can be written in the form Vt=−2Am+1,x, where the Ai satisfy the recurrence relation Am+1,x=VAm,x+ 1/2 AmVx− 1/4 Am,xxx, it is shown that Am is a homogeneous polynomial in ∂iV/∂xi. A general combinatorial formula for the coefficients of all the monomials entering Am, up to a set of constants determined by means of a recurrence relation, is derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527536
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  • 4
    Electronic Resource
    Electronic Resource
    Coefficients of fractional parentage in the L–S coupling scheme (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1368-1388 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An efficient procedure for the evaluation of the coefficients of fractional parentage (cfp's) for L–S coupled wave functions is presented. The cfp's are calculated separately for N particles, each with angular momentum l (s), coupled into a total angular momentum L (S). The N-particle states formed can belong to any permutational symmetry. The procedure for the evaluation of the L and the S cfp's for arbitrary permutational symmetry is a generalization of the procedure proposed by Bayman and Lande [Nucl. Phys. 77, 1 (1966)] for symmetric and antisymmetric states. It involves the construction and diagonalization of the matrices representing the quadratic Casimir operators for the appropriate special unitary and symplectic (or orthogonal) groups. The cfp's of the antisymmetric L–S coupled states are obtained in terms of products of cfp's for L and S corresponding to conjugate representations of the symmetric group. This method is demonstrated to provide cfp's for L–S states for systems with a considerably larger number of particles than is feasible using the procedures heretofore available.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527930
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  • 5
    Electronic Resource
    Electronic Resource
    Orbital correspondence analysis in maximum symmetry: Formulation and conceptual framework (1975)
    Springer
    Theoretical chemistry accounts 40 (1975), S. 1-15 
    Details
    ISSN: 1432-2234
    Keywords: Orbital correspondence in maximum symmetry ; Woodward-Hoffmann rules
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract A recently proposed method for the analysis of the course of chemical reactions, based on the maximal use of available symmetry, is formulated as a set of procedural rules. The application of these rules is illustrated with a simple prototype reaction: CH2+C2H4 fcyclo-C3H6. They are then derived, using the formalism of time-dependent perturbation theory within the Born-Oppenheimer approximation, thus bringing out the method's underlying assumptions and its relation to the widely used Woodward-Hoffmann procedure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00547908
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  • 6
    Electronic Resource
    Electronic Resource
    The Gaussian potential: Bound states in the continuum? (1976)
    Springer
    Theoretical chemistry accounts 41 (1976), S. 321-328 
    Details
    ISSN: 1432-2234
    Keywords: Bound states ; Continuum ; Gaussian Potential
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Simple variational solutions to the problem of a single particle in a Gaussian potential well inN dimensions,N being positive and real, are investigated. The system exhibits locally bound states in the continuum, which are demonstrated to be artifacts of the variational procedure. The relevance of the conclusions to recent studies of the possible existence of bound states in the continuum is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01178000
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  • 7
    Electronic Resource
    Electronic Resource
    Fermi and Coulomb correlations in the 21 S state of the helium isoelectronic sequence (1977)
    Springer
    Theoretical chemistry accounts 45 (1977), S. 61-67 
    Details
    ISSN: 1432-2234
    Keywords: Fermi and Coulomb correlations ; Helium isoelectronic sequence, 21 S state
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The Fermi and Coulomb holes of the 21 S state of the helium isoelectronic sequence are investigated. Several interesting differences between the results obtained and those which might be expected on the basis of the corresponding 23 S state are pointed out and discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00551459
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  • 8
    Electronic Resource
    Electronic Resource
    Generalized perturbation theory: Quality of the first-order wave function (1977)
    Springer
    Theoretical chemistry accounts 44 (1977), S. 201-213 
    Details
    ISSN: 1432-2234
    Keywords: Generalized perturbation theory ; First-order wave function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract A recently proposed version of generalized perturbation theory, in which the whole energy correction is taken care of in second order, is investigated with respect to the quality of its first-order wave function. It is demonstrated that the overlap of the wave function generated in this procedure with the exact solution is in most cases much closer to unity than those of the Rayleigh-Schroedinger or Brillouin-Wigner perturbation theories. Certain approximations, by means of which realistic systems become amenable to investigation within the presently discussed framework, are studied.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00549102
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  • 9
    Electronic Resource
    Electronic Resource
    Bonding criteria for diatomic molecular orbitals and inter-relations among them (1977)
    Springer
    Theoretical chemistry accounts 46 (1977), S. 173-181 
    Details
    ISSN: 1432-2234
    Keywords: Diatomic molecules, bonding criteria for ∼ ; Orbital energies
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Bonding criteria for molecular orbitals in diatomic molecules are discussed. An orbital force criterion is shown to have several conceptual and practical advantages, providing a basis for the investigation of inter-relations among many of the commonly employed criteria. It is found that interconsistency among those criteria is guaranteed, within the framework of Koopmans' Theorem, if the orbital energies are monotonic in the range (R e, ∞). The application of the orbital force criterion to the second row homonuclear diatomics exhibits reasonable chemical trends concerning the valence-shell orbitals, as well as indications of a slightly antibonding nature of the inner orbitals.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00578227
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  • 10
    Electronic Resource
    Electronic Resource
    Isospectral transformations in relativistic and nonrelativistic mechanics (1987)
    Springer
    Letters in mathematical physics 13 (1987), S. 141-146 
    Details
    ISSN: 1573-0530
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The modified Korteweg de-Vries hierarchy of partial differential equations generating transformations of the one-dimensional Dirac equation, is shown to reduce in the limitc→∞ to the Korteweg de-Vries hierarchy, generating isospectral transformations of the Schrödinger equation. The former hierarchy reduces into relativistic and the latter into nonrelativistic isoperiodic transformation in the limitħ→0.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00955203
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