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  • 1
    Electronic Resource
    Electronic Resource
    The relativistic Hermite polynomial is a Gegenbauer polynomial (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1549-1554 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the polynomials introduced recently by Aldaya, Bisquert, and Navarro-Salas [Phys. Lett. A 156, 381 (1991)] in connection with a relativistic generalization of the quantum harmonic oscillator can be expressed in terms of Gegenbauer polynomials. This fact is useful in the investigation of the properties of the corresponding wave function. Some examples are given, in particular, related to the asymptotic behavior and to the distribution of zeros of the polynomials for large quantum numbers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530606
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  • 2
    Electronic Resource
    Electronic Resource
    An expansion of the hypergeometric function in Bessel functions (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 5910-5914 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An expansion of the hypergeometric function 2F1(a,b,c+1;−z2/4ab) in Bessel functions of argument z is derived. This expansion can be used to obtain an asymptotic expansion of the hypergeometric function for large absolute values of a and b. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1415431
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  • 3
    Electronic Resource
    Electronic Resource
    Some results in non-commutative ergodic theory (1972)
    Springer
    Communications in mathematical physics 26 (1972), S. 247-258 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We study some properties of invariant states on aC*-algebraA with a groupG of automorphisms. Using the concept ofG-factorial state, which is a “non-commutative” generalization of the concept of ergodic measure, in general wider in scope thanG-ergodic state, we show that under a certain abelianity condition on (A,G), which in particular holds for the quasi-local algebras used in statistical mechanics, two differentG-ergodic states are disjoint. We also define the concept ofG-factorial linear functional, and show that under the same abelianity condition such a functional is proportional to aG-ergodic state. This generalizes an earlier result for complex ergodic measures.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01645093
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  • 4
    Electronic Resource
    Electronic Resource
    Some remarks on the perturbation and variation-perturbation calculations of the free energy for quantum systemsDedicated to Professor Ivar Waller. (1989)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 35 (1989), S. 839-850 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A generalization of the Gibbs-Bogoliubov inequality F ≤ F0 + 〈H - H0〉0 for the free energy F is studied which leads to a variation principle for this quantity that may be of importance in certain computational applications to quantum systems. This approach is coupled with a study of the perturbation expansion of the free energy for a canonical ensemble with H = H0 + λV in the general case when H0 and V do not commute. The second- and high-order derivatives of the free energy with respect to the perturbation parameter λ are calculated. From the second-order term is finally obtained a second-order correction to the previous variational minimum for the free energy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560350619
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