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Ho Jing Kim
- Journal of the Korean Chemical Society
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- v.20 no.3
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- pp.198-205
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- 1976
The integral Hellmann-Feynman Theorem of Parr is generalized to give a full significance to the off-diagonal form, and certain aspects of it are discussed. By use of the generalized form of the theorem, effects of configuration interaction to the crystal field theory are examined, taking perturbation energies of all order collectively into account. Thus, it is shown that there do not exist, especially when the field is strong, the radial integral which is common to all states characterized by ${\Gamma}$, S and m, and could be parametrized. If, however, one restricts the perturbing excited states only to those angularly undistorted and radially equally distorted, there results simple scaling of the crystal field parameter 10 Dq and Condon-Slater parameter $F^n$ defined within the framework of the classical crystal field theory.
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Cho, Dong Hyun
- Kyungpook Mathematical Journal
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- v.52 no.4
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- pp.413-431
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- 2012
Let $C^r[0,t]$ be the function space of the vector-valued continuous paths $x:[0,t]{\rightarrow}\mathbb{R}^r$ and define $X_t:C^r[0,t]{\rightarrow}\mathbb{R}^{(n+1)r}$ and $Y_t:C^r[0,t]{\rightarrow}\mathbb{R}^{nr}$ by $X_t(x)=(x(t_0),\;x(t_1),\;{\cdots},\;x(t_{n-1}),\;x(t_n))$ and $Y_t(x)=(x(t_0),\;x(t_1),\;{\cdots},\;x(t_{n-1}))$, respectively, where $0=t_0$ < $t_1$ < ${\cdots}$ < $t_n=t$. In the present paper, using two simple formulas for the conditional expectations over $C^r[0,t]$ with the conditioning functions $X_t$ and $Y_t$, we establish evaluation formulas for the analogue of the conditional analytic Fourier-Feynman transform for the function of the form $${\exp}\{{\int_o}^t{\theta}(s,\;x(s))\;d{\eta}(s)\}{\psi}(x(t)),\;x{\in}C^r[0,t]$$ where ${\eta}$ is a complex Borel measure on [0, t] and both ${\theta}(s,{\cdot})$ and ${\psi}$ are the Fourier-Stieltjes transforms of the complex Borel measures on $\mathbb{R}^r$.
https://doi.org/10.5666/KMJ.2012.52.4.413 인용 PDF KSCI

Khokhlova, Svetlana S.;Agmon, Noam
- Bulletin of the Korean Chemical Society
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- v.33 no.3
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- pp.1020-1028
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- 2012
This work compares various models for geminate reversible diffusion influenced reactions. The commonly utilized contact reactivity model (an extension of the Collins-Kimball radiation boundary condition) is augmented here by a volume reactivity model, which extends the celebrated Feynman-Kac equation for irreversible depletion within a reaction sphere. We obtain the exact analytic solution in Laplace space for an initially bound pair, which can dissociate, diffuse or undergo "sticky" recombination. We show that the same expression for the binding probability holds also for "mixed" reaction products. Two different derivations are pursued, yielding seemingly different expressions, which nevertheless coincide numerically. These binding probabilities and their Laplace transforms are compared graphically with those from the contact reactivity model and a previously suggested coarse grained approximation. Mathematically, all these Laplace transforms conform to a single generic equation, in which different reactionless Green's functions, g(s), are incorporated. In most of parameter space the sensitivity to g(s) is not large, so that the binding probabilities for the volume and contact reactivity models are rather similar.
https://doi.org/10.5012/bkcs.2012.33.3.1020 인용 PDF KSCI

Kun Soo Chang;Young Sik Kim;Il Yoo
- Communications of the Korean Mathematical Society
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- v.12 no.3
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- pp.579-595
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- 1997
In this paper, we establish an $L_p$ analytic Fourier-Feynman transform theory for a class of cylinder functions on an abstract Wiener space. Also we define a convolution product for functions on an abstract Wiener space and then prove that the $L_p$ analytic Fourier-Feyman transform of the convolution product is a product of $L_p$ analytic Fourier-Feyman transforms.
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Sharma, Rajendra P.
- Kyungpook Mathematical Journal
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- v.46 no.3
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- pp.307-313
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- 2006
In this paper, we first establish an interesting new finite integral whose integrand involves the product of a general class of polynomials introduced by Srivastava [13] and the generalized H-function ([9], [10]) having general argument. Next, we present five special cases of our main integral which are also quite general in nature and of interest by themselves. The first three integrals involve the product of $\bar{H}$-function with Jacobi polynomial, the product of two Jacobi polynomials and the product of two general binomial factors respectively. The fourth integral involves product of Jacobi polynomial and well known Fox's H-function and the last integral involves product of a Jacobi polynomial and 'g' function connected with a certain class of Feynman integral which may have practical applications.
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