從ATP分子水解產生的能量在α螺旋蛋白質分子以Davydov孤立子的形式傳遞，Davydov孤立子是最頂級攜帶能量的載子，傳遞過程中不會有顯著的能量耗散，而推導Davydov孤立子的運動方程式，而這些都在絕對溫度等於零的情況。我們會先說明Davydov孤立子是如何產生的以及Davydov孤立子的功能和機制。既然Davydov孤立子是以激子和聲子組成的，我們就推導其Hamiltonian然後定義出激子和聲子的試探函數。
既然聲子是相干的，我們先討論最小不確定態和相干態。接下來我們開始推導其離散形式的運動方程式，然後我們再把這運動方程式變成連續的形式。然後我們先猜一種函數的形式代入這運動方程式就得到一個非線性Schrodinger方程式，而這個方程式有孤立子解。我們把這個解代入這個非線性Schrodinger方程式及相干聲子的Hamiltonian期望值。最後，我們得到Davydov孤立子的能量值，而此能量是和Davydov孤立子的速度有關。我們得出的結果和Davydov的結果一致。
最終，我們會簡單地介紹一下絕對溫度不等於零的情況。在這種情況下，又多了實聲子的Hamiltonian項，是描述穩定非局域態的，可以互相作疊加而形成不穩定態，造成Davydov孤立子的生命週期是有限的。

We derive the equations of motion of the Davydov solitons which are perfect carriers of the energy of hydrolysis of the molecules ATP(Adenosine Triphosphate) along α-helical protein molecules without significant energy loss when T = 0K. We first illustrate how the solitons are produced and the mechanism or the function of solitons. Since the solitons are formed by excitons and phonons, we derive the Hamiltonian and define the trial wave functions for excitons and phonons.
Since the phonons are coherent, we first discuss the minimum uncertainty state and the coherent state. Next, we start by deriving the equations of motion in discrete form for the system, and then we rewrite the equations of motion in continuous form. Then, we guess a form of function to substitute into the equations of motion and we get a non-linear Schrodinger equation which has a soliton solution. We substitute the solution into the non-linear Schrodinger equation and the Hamiltonian expectation value of the coherent phonons. Finally, we derive the energy of the soliton as a function of the velocity of the soliton. Our results agree with the literature on Davydov solitons.
Finally, we will briefly introduce the condition of T ≠ 0K. In this situation, there exists a Hamiltonian term of real phonons that describes the stationary nonlocalized states which can be superimposed to form the nonstationary states causing the soliton to have a finite lifetime.

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