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研究生:許育禎
研究生(外文):Xu, Yu-Zhen
論文名稱:氫分子離子在可穿透表面附近的量子狀態研
論文名稱(外文):A Study of the Quantum States of a Hydrogen Molecule Ion Near s Penetrable Surface
指導教授:楊棨楊棨引用關係
指導教授(外文):Chi Yang
學位類別:碩士
校院名稱:淡江大學
系所名稱:物理研究所
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:1997
畢業學年度:85
語文別:中文
論文頁數:101
中文關鍵詞:原子分子離子量子狀態固體表面薛丁格方程物理
外文關鍵詞:MoleculeIonQuantum StatesSolid State SurfaceSchrodinger EquationPHYSICS
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A hydrogen molecule ion located near a surface penetrable for
electrons is considered in the prolate spheroidal coordinate
system. The properties of the electron wave function such as
singularity, convergence, symmetry and number of nodes are
analyzed. Two methods, namely, the continued fraction method and
the determinant method, for calculating the conserved quantity
A' are discussed. An asymptotic series solution of the
Schrodinger equation is obtained and this solution is applied to
investigate the problem of penetrablesurface. It is shown that
the wave function and conserved quantities of the hydrogen
molecule ion turn to the corresponding ones of a helium ion as
the distance between the hydrogen molecule nuclei approaches to
zero. The electron wave function of the hydrogen molecule ion is
represented as a linear combination of the eigen functions of
energy, operator A' and the z-component Lz of the angular
momentum. The method is based on the numerical selection of the
eigen energy and the combination coefficients to satisfy the
boundary condition as accurate as possible. When a hydrogen
molecule ion confined by a closed surface, the energy increases
and the equilibrium bond length becomes shorter.

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