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harmonic oscillator 【電學】諧(波)振(蕩)器。

harmonic progression

By use of the relationships between the hermite polynomial and the laguerre polynomial , the eigenequations of one - dimensional harmonic oscillator and hydrogen atom are conversed into the same equations in form . therefore the relationships between energy levels and wave functions of one - dimensional harmonic oscillator and hydrogen atom are found . through the coordinates transform , the relationships between energy levels and wave functions of two - dimensional harmonic oscillator and hydrogen atom are found 首先綜述了諧振子與氫原子的基本理論的研究現狀,并在此基礎上對諧振子與氫原子的關系展開了研究,通過厄密特方程與拉蓋爾方程的相互轉化,將一維諧振子與一維氫原子的本征值方程轉化為相同形式的方程,從而比較得出它們能量及波函數間的關系,并通過坐標變換將直角坐標系下二維氫原子的本征值方程轉化成與曲線坐標系下二維諧振子的本征值方程相同的形式,從而得出二維氫原子與二維諧振子的能量及波函數的關系。

Coordinate transformation , matrix , vectors , newton ' s law , conservation theorems , simple harmonic oscillator , non - linear oscillations , gravitation , euler ' s equation when auxiliany condition are imposed , the delta notation , lagrangian and hamilitonian dynamics , central - force motion , dynamics of a system o f particles , motion of noninertial reference frame , dynamics of rigid body , coupled oscillations , orthogonality of the eigenvectors , continuous system 座標變換、矩陣、向量、牛頓定律、守恒定律、簡諧振動、非線性振動、引力、尤拉式方程式及附加條件、符號、拉格蘭及漢米爾頓力學、中心運動、多粒子系統動力學、非慣性參考座標運動、剛體動力學、耦會振動、本微向量正交性、連續系統。

Quark medium is regarded as non - harmonic oscillator model , discussing its response to su ( 2 ) non - abelia field , the perturlation expansion method is used to find the first , second and third order approximate solutions to the response equation , and some nonlinear features of the response are preliminarily displayed 將夸克介質視為非簡諧振子模型,討論了它對su ( 2 )非阿貝爾場的響應,采用微擾迭代法解出了方程的一、二、三級近似解,初步得出了這種響應的一些非線性特征

At the same time in terms of su ( 1 , 1 ) algebra , the eigenequations of two and three - dimensional harmonic oscillator and hydrogen atom with inverse square potential are conversed into the same equations in form . then the relationships between energy levels and wave functions of them are found 同時本文利用su ( 1 , 1 )代數將二維、三維情況下的諧振子同加了反平方勢的氫原子分別表示成具有相同形式的兩算符下的本征值方程,從而得出他們的能量對應關系。

We explore a creative teaching method . by making use of harmonic oscillator model and single pendulum model . single pendulum model is good for learners to find a solution to a problem , and it helps to forming good cognitive structure 重點是利用彈簧振子和單擺兩個模型對《機械振動》單元教學進行的新探索,同時介紹了利用單擺模型幫助學生解決物理問題,形成良好知識結構的實例。

By using some formulae of confluent hyper - geometric function , the results of radial operators on the normalizing radial wave function of a 3 - d isotropic harmonic oscillator are derived , and the ladder operators are given to calculate the matrix elements 摘要利用合流超幾何函數的遞推關系式得到徑向算符對歸一化徑向函數的作用結果,得出其升降算符通項,便于求解矩陣元。

We solve the master equation by system - reservoir method with born - markov approximation for the composite system with one simple harmonic oscillator and the reservoir composed with many other harmonic oscillators surrounded 摘要:我們使用系統與熱庫的方法,并使用波恩-馬可夫近似來求解一模型:單一簡諧振子與一群簡諧振子的熱庫。

The excellence and basic thinking of green function method is shown because forced harmonic oscillator is discussed , further more , that the green function method is used widely is clarified 最后,以普通物理中的受迫諧振子問題為例,突出體現了green函數方法的優點,并進一步說明了green函數方法應用的普遍性。

A damped harmonic oscillator without a driving force was studied using canonical tramsformation ; an exact wavefunction and energy level for the damped harmonic oscillator has been obtained 摘要對于無外界驅動力且阻力與速度成正比的阻尼諧振子,通過正則變換,得出了阻尼諧振子的嚴格波函數及其相應能級。

For small displacement u , the oscillator is a duffing - type cubic non - linear oscillator , while for large displacement u , the oscillator approximates to a linear harmonic oscillator 所謂達芬諧波振子是指當位移遠小于1時,系統可化為三次非線性振子,而當位移遠大于1時,該系統則化為線性諧波振子。

At last , about how to improve teaching harmonic oscillator and hydrogen atom in quantum mechanics is briefly reviewed on base of modern teaching theory and self - study experience 最后結合現代教育理論及本人的學習體會對諧振子與氫原子的教學研究進行了簡單討論。

Solutions to schroedinger ' s equation in one dimension : transmission and reflection at a barrier , barrier penetration , potential wells , the simple harmonic oscillator 維薛丁格方程式的解:位壘的穿透及反射,位壘滲透,位能井,簡諧振子。

Some kinds of the supersymmetric quantum mechanics systems related to the three - dimensional isotropic harmonic oscillator 三維各向同性諧振子的超對稱量子力學體系

This paper deals with analytical approximate solutions to the duffing - harmonic oscillator by a new method 摘要用一種新方法研究達芬諧波振子的解析逼近解。

Energy relation between two - dimensional harmonic oscillator and hydrogen atom in inverse square potential 二維諧振子與加反平方勢的二維氫原子的能量關系

The deductive method for the operator theory of the uncertainty relation of one - dimensional harmonic oscillator 一維諧振子不確定關系的算符理論推導法

Energy relation between three - dimensional harmonic oscillator and hydrogen atom in ubverse square potential 三維諧振子與加反平方勢的三維氫原子的關系

Quantum operator methods associated with canonical transformation for 1d harmonic oscillator problem 哈密頓算符的對角化與能量本征值問題的代數解法

Energy levels of single particle in 3 - dimensional and symmetrical deformed harmonic oscillator potential energy 軸對稱變形諧振子勢中的單粒子能譜