共查询到17条相似文献,搜索用时 73 毫秒
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经典力学中把L=r×P叫做角动量.量子力学将r和P看作算符后得到算符(1)(V是微分算符),称L为角动量算符.由定义式(1)出发,经过微分运算可得到角动量算符不同分量间的对易关系(2a) (2b) (2c)这种关于角动量的定义和对易关系的推导方法,不具有普遍意义,它只适用于轨道角动量.而角动量这个量跟系统在转动下的变换性质有本质联系.角动量的对易关系,与体系在转动下的特性密切相关.笔者认为,在量子力学的教学中,如果在利用经典概念建立了量子力学的轨道角动量算符后,能再进一步从体系的转动变换性质推导角动量算符,并给出角动量的一般定义式,对提… 相似文献
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在量子力学教材中,坐标算符在动量表象中的表示只是给出最终的结果,很少提及其详细的推导过程,这将使学生在学习量子力学过程中产生相应的疑惑.还有的是利用自由粒子是平面波的基本假设和狄拉克δ函数来推导坐标算符在动量表象中的表示,比较抽象和复杂,在教学中不利于学生的深入理解.本文另辟新径通过在泰勒展开的基础上引入了泰勒平移的概念,最后根据对易关系和泰勒平移来推导坐标算符在动量表象中的表示.该方法在教学过程中具有启发性,更有利于学生对这部分内容的理解. 相似文献
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从三十年代冯·诺伊曼等人的工作开始,量子力学逐渐被看成是一些公理组成的数学体系.量子力学基本公理主要有以下几个: 1.一切微观状态为希尔伯特(Hilbert)空间中的矢量; 2.可观察量相应算符为希尔伯特空间中的线性厄密算符; 3.可观察量与相应算符存在如下关系(本征态情况):其中P──算符,p──相应可观察量,──希尔伯特空间矢量; 4.可观察量的平均值用下式表示(非本征态情况): 从这些公理出发,可以获得量子力学各种重要成果.但是,这些公理看来似乎没有直接的物理意义,因此,资产阶级学者们就利用这一点对量子力学进行歪曲,把量子力学说成… 相似文献
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对约束在曲面上粒子运动的描述可以在内部坐标即曲面局部坐标下进行,也可以在外部坐标即在笛卡尔坐标下进行.在量子力学中,动量和动能算符的表示在这两种描述中各有不同,前者的动量算符仅包含内禀几何量,后者的动量算符包含了曲面的平均曲率.考虑到算符次序问题,动能算符对动量算符的依赖关系也不同,前者的依赖关系仅发现存在一种,后者的依赖关系已经发现有两种.
关键词:
量子力学
微分几何 相似文献
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四、抽象向量法上述算符法虽然将某些运算作为算符来处理,并建立了一些算符之间的代数关系,但没有利用向量空间的概念。在下面的方法中,基于与量子力学的类比,明确地提出了一个抽象向量空间,从而将量子力学的方法移到傅里叶光学中来。 1.单色波传播方程的傍轴近似 相似文献
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Carl M. Bender 《Czechoslovak Journal of Physics》2004,54(10):1027-1038
It has recently been shown that a non-Hermitian Hamiltonian H possessing an unbroken PT symmetry (i) has a real spectrum that is bounded below, and (ii) defines a unitary theory of quantum mechanics with positive norm. The proof of unitarity requires a linear operator C, which was originally defined as a sum over the eigenfunctions of H. However, using this definition it is cumbersome to calculate C in quantum mechanics and impossible in quantum field theory. An alternative method is devised here for calculating C directly in terms of the operator dynamical variables of the quantum theory. This new method is general and applies to a variety of quantum mechanical systems having several degrees of freedom. More importantly, this method can be used to calculate the C operator in quantum field theory. The C operator is a new time-independent observable in PT-symmetric quantum field theory. 相似文献
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Paul Bracken 《International Journal of Theoretical Physics》2003,42(4):775-781
A geometric connection between quantum mechanics and classical mechanics is described and an operator version of the Poisson bracket is developed. 相似文献
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Vladimir Dzhunushaliev 《Foundations of Physics Letters》2006,19(2):157-167
A non-associative quantum mechanics is proposed in which the product of three and more operators can be non-associative one.
The multiplication rules of the octonions define the multiplication rules of the corresponding operators with quantum corrections.
The self-consistency of the operator algebra is proved for the product of three operators. Some properties of the non-associative
quantum mechanics are considered. It is proposed that some generalization of the non-associative algebra of quantum operators
can be helpful for understanding of the algebra of field operators with a strong interaction. 相似文献
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Nivaldo A. Lemos 《Physics letters. A》1980,78(3):239-241
Davidson's construction of a Hilbert space and of quantum operators on the basis of the Fényes-Nelson stochastic mechanics is extended to the case in which a dissipative force linear in the velocity is present. The hamiltonian becomes a nonlinear operator but the position and linear momentum operators are the same as in ordinary quantum mechanics. 相似文献
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主要从量子力学发展史,量子力学概念,多媒体技术运用,以及针对工科专业的实际应用4个方面,对工科专业的量子力学教学方法进行了探索,激发学生学习量子力学的兴趣,提高教学质量. 相似文献
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Jack Cohn 《International Journal of Theoretical Physics》1983,22(1):19-28
A formulation of nonrelativistic, spinless, quantum mechanics is presented which is based on four postulates. Three of the postulates are very analogous to relations that hold in an operator formulation of classical mechanics, and the fourth is that the wave function evolves linearly in time. The conventional statistical assertions of quantum theory as well as the Schrödinger equation are recovered. 相似文献