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학술발표회초록보기

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  • 09월 04일 17시 이후 : 초록수정 불가능, 일정확인 및 검색만 가능

제114회 대한화학회 학술발표회, 총회 및 기기전시회 안내 Some Simple Ideas in Perturbation Theories

등록일
2014년 9월 12일 11시 14분 15초
접수번호
1539
발표코드
AWARD-1 이곳을 클릭하시면 발표코드에 대한 설명을 보실 수 있습니다.
발표시간
금 09시 : 00분
발표형식
기념강연
발표분야
기념강연
저자 및
공동저자
이상엽
서울대학교 화학부, Korea
In this talk, I will present two general methods in the perturbation theories that would be useful in statistical mechanics and quantum mechanics.
The first one is a new method of solution for the Fredholm integral equations of the second kind. The method would be useful when the direct iterative approach to the integral equation leads to a divergent perturbation series solution. In such case one usually employ the Padé approximation, but we have found that our method gives much more accurate results than Padé approximation method for the same computational cost. A main advantage of the new method comes from the fact that the solution has the same structure as the exact solution. By using the method, we have derived a very accurate expression for the steady-state rate constant of diffusion-influenced bimolecular reactions involving long-range reactivity. We consider the general case in which the reactants interact via an arbitrary central potential and hydrodynamic interaction. The rate expression becomes exact in the two opposite limits of small and large reactivity, and also performs very well in the intermediate regime.
The second one is a variant of the Brillouin-Wigner perturbation theory, which can be easily extended to the quasi-degenerate case. A main advantage of the new theory is that the computing time required for obtaining the successive higher-order results can be made to be minimal after the fourth-order calculation. We illustrate the accuracy of the new perturbation theory for some simple model systems like the perturbed harmonic oscillator, the perturbed particle in a box, and the electronic problems of very small molecular systems.

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