中文摘要

論文題目：人造雙原子分子結構
研 究 生：黃冠銘
指導教授：邱輝煌

現今科技已邁向奈米尺度，甚至更小的尺度也已逐漸發展成形中；在理論科學中，量子力學對於微小粒子的描述已有相當的探討與佐證，它跳脫古典力學的侷限給了人們一個面對微小尺度的解決方案與新思維，有藉於此，人們對於量子力學領域的探索與理解更顯得於日劇增，本論文係以量子力學下的理論架構來延伸探討這相關性的課題。迄今仍然沒有充分的解釋去說明一個雙分子原子在量子位勢能下的量子能的來源、位勢能的平衡和渦流引起的動能。所以，我們需要建立一個原理，該原理是介於外在位勢與內應力間所構成的力學平衡原理，且在其所引起的量子位勢之相依梯度下去儲存原子與雙分子結構與力學的穩定度。邱輝煌老師發展一套簡要且完整的理論，該統御理論稱為量子相伴原理(Quantum Concomitance Principle)，利用此原理可以解釋幾個簡短重要的主要模式(Principal Mode)的相伴關係，並利用量子模式平衡關係(Quantum Modal Balance)來找出原子及分子的結構、量子能、粒子的動態運動與外在位勢，彼此相互之間能量平衡的關係式。
本研究所運用的方法便是利用量子相伴原理來分析解構人造雙原子分子在特定分子位能作用下之結構、動態平衡與量子能，包含(1)奠基在量子擴散理論下量子相伴原理如何提供分析分子內量子模式平衡理論 (2)探討分子在一給定分子位能作用下之結構、能量與動態特性
結果顯示出相伴原理提供具有特定量子勢能在不同模式間之一對一相對應關係，另外，我們可以從機率密度分布的曲線觀察出與簡諧振子相似的有趣物理現象。本分析顯示特定分子位能造就分子內特定量子機械限制，進而阻礙其他量子態下之能量分佈，本研究之分子中之量子模式平衡理論可擴展用於人造分子之設計。

ENGLISH ABSTRACT

Subject: Artificial Diatomic Molecular Structures
Student: Guan-Ming Huang
Advisor: Huei-Huang Chiu

Three profound issues, which remain un-addressed or imperfectly understood, are the physical origin of the quantized energy of a diatomic molecule, and the balance of the potential energy, and the kinetic energy of the vortex induced flow with the quantum potential energy. We need a principle to establish dynamic equilibrium between the external potential force and the inner field stresses, induced by a corresponding gradient of the quantum potential to preserve structural and dynamic stability of atoms and molecules. Professor H.H.Chiu revealed that the structure, quantized energy, dynamic motion of particles, external potential, defined in short as the principal modes all the atoms and molecules are governed by the “quantum concomitance principle”.
The study presents the quantum concomitance principle analytical investigation and the results describing the structure, dynamic balances and quantized energy of an artificial diatomic molecule with a specific molecule potential. We show (1) how the “quantum concomitance principle” serves to the formulation of a self-contained molecular modal balance theory, based on quantum diffusive dynamics. (2) the structure, energetic and dynamics of particles under prescribed external potential.
The results show that the quantum concomitance principle gives one-to-one correspondence between each principle mode with a corresponding quantum potential. We can observe that, the experiment data of probability density, it looks like similarity of the harmonic oscillator. The analysis shows that there are certain quantum mechanical limitation in the type of potential which prohibit the distribution of quantum states. These are to be considered in the design of the artificial molecules.

REFERENCES

[1] H.H. Chiu, “Quantum Fluid Mechanical and Electronic Structure Of A Hydrogen-Like Atom,” Proceedings of the royal society society:A, vol.461 ,pp.3023-3057, (2005).
[2] D. J. GRIFFITHS, “Introduction to Quantum Mechanics” 2nd, Pearson Prentice Hall, (2005)
[3] H.H. Chiu, H.L. Tsai. and Y.C. Wang, “Artificial Diatomic Molecular Structures”, AASRC/CCAS Joint Conference, (2005)
[4] Y.C. Wang, “Vibrational Modal Energy Balance Of A Diatomic Molecule”, Master Thesis, institution of aeronautics and astronautics National Cheng-Kung University, (2003)
[5] Y.F. Peng, “Energetic And Dynamic Analysis In Simple Harmonic Oscillator”, Master Thesis, institution of aeronautics and astronautics National Cheng-Kung University, (2004)
[6] R. Eisberg & R. Resnick, “Quantum Physics Of Atoms, Molecules, Solids, Nuclei, and particles” ,Wiley, (1985)
[7] L. D. Landau & E. M. Lifshitz, “Quantum Mechanics Non-Relativistic Theory”3rd ,
Oxford : Pergamon Press, (1977)
[8] A. Goswami, “Quantum Mechanics” 2nd , Wm. C. Brown Publishers, (1997)
[9] D.D. Fitts, “Principle of Quantum Mechanics as Applied to Chemistry and Chemical
Physics” Cambridge University Press (1999)
[10] E. Merzbacher, “Quantum Mechanics”3rd , John Wiley & Sons, (1998)
[11] M. D. Fayer, “Elements of Quantum Mechanics”, Oxford University Press, (2001)
[12] R. W. Robinett, “Quantum Mechanics ” , Oxford University Press, (1997)
[13] G. M. Barrow, “Introduction To Molecular Spectroscopy”, McGraw-Hill Press, (1962)
[14] C. D. Yang, “Wave-Particle Duality In Complex Space”, Annals of Physics, Vol.319, PP. 444–470 , (2005)
[15] C. D. Yang, “Quantum Dynamics of Hydrogen Atom in Complex Space”, Annals of Physics , Vol.319, PP.399–443 , (2005)
[16] P. M. Morse, “Diatomic Molecules According to Wave Mechanics. II. Virbrational Levels”, Vol.34, PP.57-64 , (1929)
[17] A. D. Alhaidari, “Solution of the Relativistic Dirac-Morse Problem”, Vol.87, Number 21, (2001)
[18] C.A.Rouse, “Series Solution of the Schrödinger equations with the Morse Potential”, 3rd series, Vol. 36, Number 1, (1987)