本論文旨在探討多管電子奈米噴流的能量以及在不同雷諾數之下所產生的結構行為與變化。由於波的傳遞、交互作用、穿隧等量子效應的影響之下，造成本次所探討的多管奈米噴流不同於傳統的噴流。在具有規律性間隔的多管噴流之中，量子波的行為是以主要跟中間的噴流分支為其特色，後者是由兩個相鄰主噴流的交錯之下所產生的。在低雷諾數之下，噴流結構的變化主要是以兩個不同的方式來發生：第一，主要與中間分支的噴流兩者皆顯現出高機率密度的鑽石形狀區域以及低機率密度的暗沉區域，隨著雷諾數的增加，主噴流會沿著軸向方向而延伸而中間分支的噴流則會朝著下游方向來偏移，在高雷諾數之下，鑽石型的結構也會向著下游方向來產生偏移。第二，鑽石形結構的尺寸也會隨著雷諾數之增加而增大。噴流結構的變化主要歸因於波特性方面變化以及和de Broglie波長兩著間的合成效應。另一個頗為顯著且令人感到有興趣的特色為每一道噴流在高機率密度之下所產生的量子叢集。由波的干涉現象所激起的鑽石結構以及量子多管奈米噴流的叢集過程提供了我們對於不同奈米裝置的應用，例如可以設計用來做深層太空任務的高比衝量多管奈米噴流推進的推進器、對於微米以及奈米引擎的燃料供給、奈米級的藥品注射和量子感測器等相關奈米製造。

　　在本論文最後，我們採用數值分析的方法來計算在我們選定的噴流出口處沿著x下游方向對於多管量子奈米噴流的波函數以及機率密度的值。我們採用二階、四階的有限差分法以及Runge-Kutta數值方法來求解描述本物理問題與時間變數相關的薛丁格方程式，另外，我們採用Symmetric Conjugate Gradient的方法來求解描述本物理問題不與時間變數相關的薛丁格方程式。最後我們會發現在局部解析解以及這些數值方法當中所顯示出來的計算結果在我們比較的部分皆有相同的趨勢。

　　Energies, structural behaviors and their variation in a broad rage of quantum Reynolds number of multi-slit electron nanojets are examined. Multi-slit nanojets are strikingly different from the classical jets because of the quantum effects which include the propagation, interaction and tunneling of quantum waves. In a regularly spaced multi-slit jets, the quantum wave behaviors are featured by the interposed primary and center jet branches, the latter of which is created by the intersection of two adjacent primary jets. At low Reynolds number, the variation in jet structure occurs in two distinct manners: First the primary and center branch jets both exhibit a family of diamond-shaped high density regions and lower density shadowed regions. By increasing Reynolds number, the primary jets extend in axial direction and the center branch shift downstream direction. The diamond shaped structures also shift toward the downstream at large Reynolds number say N = 100. Secondly, the size of diamond shaped structure increases at high Reynolds number. The variation in the jet structure is attributed to the combined effects of the variations in the direction of wave characteristics,and the de- Broglie wavelength. Another rather remarkably interesting feature is the quantum-clustering, featured by the formation of high probability density occurs in each jet. Complexities in diamond structures, and clustering processes in quantum multi-nanojet manifestly provoked by wave interference lend themselves to provide various nanodevice applications: high specific impulse multi-nanojet propulsive thrusters for deep space missions, lithography, nanomanufacturing, fuel injection for micro and nanoengines, nanoelectronics, drug delivery, and quantum sensors.

　　At the last chapter of this thesis, the numerical analysis is developed to give another method to evaluate the wave solution and the probability density of the multi-slit quantum nanojets at the center of our selected jet's exit. The calculation is performed along downstream x direction. We utilize Second-order, Fourth-order Finite Difference Methods and Fourth-order Runge-Kutta method to solve the time-dependent Schrodinger equation of present problem. On the other hand, we use Symmetric Conjugate Gradient method to solve the time-independent Schrodinger equation of present problem. We can find out that the results of partial analytic method and numerical methods have the same tendency in our compared regions.

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