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薛定谔波函数

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Week 15 Experiment law of hydrogen atomic spectrum, Bohr hydrogen atom theory, wave -particle dualism of matter, de Broglie waves, uncertainty relation, wave function and its statistical explanation, standard condition of wave function, Schrodingger equation in one dimension, simple introduction of quantum mechanics.

第15周氢原子光谱的实验规律,氢原子的玻尔理论;波粒二像性,德布罗意波,不确定关系;波函数及其统计解释,波函数的标准条件,一维薛定谔方程,量子力学简介。

Using cubic spline interpolation function, we construct a finite element model to approximate the nonlinear Schr〓dinger equation, and provide a complete discrete scheme with the conservation properties of mass and energy.

本章从应用角度出发,着重讨论孤波形式的解的计算,为此我们利用三次样条函数的插值基函数构造出非线性薛定谔方程的一个有限元离散模型,给出了具有保质量与能量守恒的全离散计算格式。

By solving the Schrodinger equation and using the boundary conditions of delta function, We can get the Buttiker scattering Matrix.

通过解薛定谔方程求得自旋空间的波函数,再由边界条件确定波函数的振幅,进而求出散射矩阵。

With a unitary transformation, the Schrodinger equation becomes the standard mathieu equation, then the energy spectrum and the wave functions of the system are obtained.

用幺正变换将薛定谔方程变换为标准的马丢方程,通过对薛定谔方程的求解,得到了系统的能级和波函数。

This article consists of four parts: In the first part of thesis introduced Heisenberg's early years of life and the creation of Matrix mechanics, expounded Münich、G?ttingen,Copenhagen, three places different academic atmosphere which produce to Heisenberg's institute of physics, and revealed how to set up Matrix mechanics by mathematics method; The second part introduce Schr?dinger's university life, the research results, and the establishment of Wave mechanics. The different academic atmosphere of Vienna and Zürich have the difference influence which brings to Schr?dinger's research work, how to establishment the Schr?dinger equation based on Hamilton equation of classical mechanics, and elaborated the physical controversy caused by the equivalent.; The third part analyzed two mechanics different approaches in which the way to propose the question and solve the question; The last part recommend the different philosophy interpretations, Schr?dinger's interpretation onΨfunction, the statistical interpretation of Wave mechanics, uncertainty principle, and which caused this free discussion of quantum mechanics.

文章共分为四部分:第一部分介绍了海森伯的早年生活及其创立矩阵力学的过程,阐明了慕尼黑、哥廷根、哥本哈根三地不同的学术氛围对海森伯的物理研究所产生的不同作用,并揭示了海森伯如何用数学方法建立矩阵力学方程的过程;第二部分介绍了薛定谔的大学生活、研究成果,以及波动力学的创立过程,说明了维也纳和苏黎世不同的学术气氛给薛定谔的研究工作带来的不同影响,解释了薛定谔以经典哈密顿方程为基础建立薛定谔方程的过程,并阐述了等价性所引起的物理争论;第三部分分析了两种力学的思想进路在提出问题、解决问题上的不同;最后一部分介绍了对两种力学形式不同的哲学诠释,薛定谔对Ψ函数的诠释、波函数的统计解释和测不准原理,以及由此引起的量子力学的大讨论。

The numerical solution of wave function is obtained by solving schrǒdinger equation of partical spin with symposium.

利用辛算法求解粒子自旋问题的薛定谔方程,得到波函数的数值解。

A wave function for laser dressed atom is derived as a perturbative solution of the time-dependent Schrdinger equation in the velocity gauge.

作为含时薛定谔方程的微扰近似解,在速度规范下给出了激光场中缀饰原子的一个波函数。

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