講演抄録/キーワード |
講演名 |
2014-11-17 11:40
緩やかに曲がったパイプ中の1粒子量子系のエネルギー準位の摂動計算 ○後藤振一郎(分子科学研) |
抄録 |
(和) |
断面を一定の長方形に保ちつつ、中心軸が緩やかに曲がった3次元パイプ内に非相対論的かつ量子的な質点を閉じ込めた場合のエネルギー準位を摂動法を用いて計算し、まっすぐなパイプの場合からのエネルギー準位の補正公式を求めた。系は3次元井戸型ポテンシャル中の一粒子に対するシュレーディンガー方程式に従うものとし、特に中心軸の曲がり方は古典微分幾何学で知られているフレネセレの公式で与えられるものとした。摂動法として空間的な境界条件を厳密に満たす特異摂動法を採用した。 |
(英) |
A geometrical perturbation scheme that addresses some aspects of the Schr¨odinger equation for a single particle confined in a class of curved pipes is established. For our analysis the pipe will be regarded as a perturbed finitely long hollow cuboid. The perturbation will maintain the pipe’s rectangular cross-section while deforming its axis into a planar space-curve with, in general, non-constant curvature. It is assumed that the curvature $kappa (z)$ depends on the arc-length $|z|$ of the planar space-curve. Furthermore we require that $|kappa (z)L| ≪ 1$ with $L$ being
a length of the rectangular cross-section for the perturbation analysis to be effective. It is also assumed that the confinement is modeled with the 3-dimensional infinite potential well. Under these conditions the energy spectrum of the Schr¨odinger equation for a non-relativistic particle confined with the 3-dimensional infinite potential well, corresponding to a prescribed curved pipe, will be considered. A perturbation scheme will be applied to calculate a normalized wave function and a spectrum as a perturbation expansion in powers of $L$. Mode expansions based on
Dirichlet eigen-functions of the Laplacian for a rectangular domain can be used to reduce the general problem at each order. Since it will turn out that there exist some resonance terms in the course of our perturbative analysis,
a singlar perturbation method will be employed to deal with such resonance terms. This methodology gives a perturbative expression of the energy spectrum. |
キーワード |
(和) |
シュレーディンガー方程式 / 摂動法 / 井戸型ポテンシャル / フレネセレの公式 / / / / |
(英) |
Schrodinger equation / perturbation method / infinite potential well / Frenet-Serret formulae / / / / |
文献情報 |
信学技報 |
資料番号 |
|
発行日 |
|
ISSN |
|
PDFダウンロード |
|