2) n-dimensions non-spherical harmonic oscillator potential
n维非球谐振子
3) N dimensional isotropic harmonic oscillator
N维各向同性谐振子
1.
Two recurrence formulas for radial average values of N dimensional isotropic harmonic oscillator are derived.
推导出了用于 N维各向同性谐振子径向平均值计算的二个递推关系 ,并在 - 3≤ s≤ 3的条件下 ,给出了平均值〈nr JN - 2 | r2 s| nr JN - 2 〉的值 。
4) one-dimensional harmonic oscillator
一维谐振子
1.
The deductive method for the operator theory of the uncertainty relation of one-dimensional harmonic oscillator;
一维谐振子不确定关系的算符理论推导法
2.
The method of using node theorem to solve the one-dimensional harmonic oscillator with a deta potential was presented and the reliable accurate eigenenergies and eigen- wave functions were given.
探讨了用节点法求解存在势时的一维谐振子势,并给出精确可靠的能级及本征波函数。
3.
This paper also pointed out that the lower limit of one-dimensional harmonic oscillator s ΔpΔx is exactly the lower limit of /2 which given by the general form of the uncertain relation,however the lower limi.
推出了一维谐振子的位置不确定范围、动量几率幅和动量几率密度的递推公式、动量不确定范围和等式型动量 -位置不确定关系 。
5) two-dimensional harmonic oscillator
二维谐振子
1.
In terms of SU(1,1) algebra, the relationship between energy and wave function of two-dimensional harmonic oscillator and two-dimensional hydrogen atom are discovered.
借助于ＳＵ(１,１)代数,找出了二维谐振子与二维氢原子的能量及波函数间的关系。
2.
Through the counterchanges of two methodologies of coordinates and special equations,the eigen equations of the two-dimensional harmonic oscillator and hydrogen atom are converted into the same equations in form.
通过特殊方程间的相互转换,将二维谐振子与二维氢原子的本征值方程转化为具有相同形式的两方程,从而比较得出它们波函数及能级之间的对应关系。
3.
In this paper,We work out the relationship between the energy eigenfunction,the energy eigenvalues of the two-dimensional hydrogen atom and those of the two-dimensional harmonic oscillator in terms of su(1,1) algebra.
借助于su( 1 ,1 )代数找出了二维氢原子与二维谐振子之间的能量本征值、能量本征函数的关系 ,并进一步找出了它们之间的坐标变换关
6) three dimensional harmonic oscillator
三维谐振子
1.
The approximate solution and the exact solution of three dimensional harmonic oscillator in potential H′=(λμω_0~2/2)(x~2+y~2+z~2);
三维谐振子在H′=(λμω_0~2/2)(x~2+y~2+z~2)下能级的近似解和精确解
2.
The B2 proportional term in the Hamiltonian of three dimensional harmonic oscillator in the uniform magnetic field is considered,and calculated the perturbaion matrix elements.
在考虑均匀磁场中三维各向同性谐振子哈密顿量中B2项影响的情况下,计算了均匀磁场中三维谐振子n=5能级的微扰矩阵元和一级能量修正值,并讨论了其能级简并度的解除。
3.
The article studies a simple method for any energy level of three dimensional harmonic oscillator in uniform magnetic field.
研究了任意能级下均匀磁场中三维谐振子一级能量修正值的简便方法。
补充资料：谐振子
谐振子
oscillator, harmonic
[补注1 [A正1 Arnol‘d，V 1.，Mathe皿t:cal卿th。〔15 of classlcal rnCch翻cs，Spnnger，1978(译自俄文). 【AZ 1 Seh湃L .1.，Quantum毗chanies，McGraw一Hill， 1949、杜小杨译谐振子〔蝴锐场叙丫，har~;oe““朋:rop，r叩Mo““-”ec心“1 一个单自由度系统，其振动由方程 无+田Zx二0来描述.相轨道是圆，振动的周期T=2兀/o，与振幅无关.谐振子的位能依赖于x的平方: 。2叉2 U之立竺‘竺-， 一， 谐振子的一些例子是:摆的微小振动，固定在刚性不变的弹簧上的质点的振动，最简单的电子振荡电路.“谐振子”和“线性振子”常常作为同义词使用. 量子力学线性振子的振动由阳诚戏吃er方程(Sellr6dinger eq娜戒lon) h，d，沙」「_m。，Zx，1。 一三二一二六答口十}E一二兴井一.{少“O 2小dx‘L一2」了来描述.其中m是质点的质量，E是它的能量，h是Planck常数，。是频率.量子力学线性振子具有能级离散谱:E。=(n+l/2)h。，n=0，1，2，…;相应的本征函数可以由Her而te函数(Her而te fimction)来表示. “振子”这一术语适用于其运动带有振动特性的具有有限个自由度的(力学或物理)系统(例如，vdn derPol振子—表示处于位势为坐标的正定二次型的位势力场中的质点的振动的多维线性振子，见van妞Fbl方程(van der Pol equation)).对于“振子”甚至“线性振子”，显然都没有唯一的解释.
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