量子力學和奈米技術兩者都是在科學及應用上的一項熱門且尖端的領域，它們的發展對於二十一世紀的今天，都將在經濟、國防及社會上有著重大的影響，甚至改變人們的傳統思維及生活方式。今天我們在生活中所用到的科技工具，都是以前的研究所奠定下來的基礎而發展出來的，因此沒有今天的基礎研究，就沒有明天的應用科學，也就沒有相應的開發研究。本文的主要目的是利用邱教授所發展的“量子模式平衡理論”及“量子擴散流體力學”來分析及了解在量子簡諧振動系統當中，外加勢能、量子勢能等等的能量，彼此之間的關係和相互平衡的機制以及量子系統的架構穩定性與概率流體的流動性質如何聯繫。這些分析提供了在量子系統總能量的基本知識和化學過程裡細節的洞察力，而由於概率流體的量子擴散能和量子擴張動能兩者之間的儲存、釋放及相互作用產生了各種量子現象並且使量子系統得以維持基本架構。藉由這些基本且重要的分析、研究，使得在量子系統的主要原理、定理或關係上，能有重大的突破及創新。

　　Nanosystems, atoms, and molecules possess quantized energy at each state and maintain structural stability, to preserve structural configuration. The questions of basic interest are how quantum energetic and the structural stability of a system are related with the flow properties of the probability fluid, which represents the probability density distribution of a particle in a quantum system. The knowledge offers fundamental understanding of the total energy of a system and provides detailed insights into chemical processes. The structural stability portrays the views of the structural integrity of nano-assemblying of artificial atoms, molecules and nano-machines through the nature of the balance of net forces on the particle in the system. The objectives of this paper are to show that the quantized energy of a harmonic oscillator is equal to the first type of quantum diffusion energy of the probability fluid, and the dynamic stability of an oscillator is maintained by the balance of a the forces induced by the second type of quantum diffusion energies with the particle interactive potential force, whereas the kinetic energy of the mean motion of the quantum probability fluid is supplied by the third type of quantum diffusion energy.

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