共查询到20条相似文献,搜索用时 281 毫秒
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本文用群论方法讨论了量子力学中三维各向同性谐振子的能级简并度与对称性的关系,经过运算给出了三维各向同性谐振子具有SU(3)对称性的结论. 相似文献
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利用b与b~+算符求解一维线性谐振子本征值问题 总被引:1,自引:0,他引:1
利用b与b+算符求解一维线性谐振子本征值问题①陈祖宁(南宁市广播电视大学南宁530022)1引言一维线性谐振子本征值问题,属于一维定态问题。一般量子力学教科书,都采用坐标表象的定态薛定谔方程求解。这种方法采用的数学是熟知的二阶微分方程,因此处理起来比... 相似文献
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本文先介绍用不确定关系粗略计算一维线性谐振子零点能,然后再结合普朗克量子假设给出谐振子能级公式. 相似文献
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《量子力学》自学辅导之八──狄拉克符号和占有数表象(续)曾心愉,宋宇辰,裴文杰(复旦大学物理系,复旦大学理论物理骨干教师班上海200433)2关于一维线性谐振子的讨论2.1坐标表象一维线性谐振子H算符及其本征函数在坐标表象中为式中的本征值为由厄米多项... 相似文献
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线性谐振子体系加入非谐振势后能级与本征态的求解与分析是十分重要的 ,利用数学软件Mathematica4 .0软件对其定态Schr dinger直接进行数值计算 ,能够得出精度很高的计算结果。 相似文献
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The notes here presented are of the modifications introduced in
the application of WKB method. The problems of two- and
three-dimensional harmonic oscillator potential are revisited by WKB and
the new formulation of quantization rule respectively. It is found
that the energy spectrum of the radial harmonic oscillator, which
is reproduced exactly by the standard WKB method with the Langer
modification, is also reproduced exactly without the Langer
modification via the new quantization rule approach. An
alternative way to obtain the non-integral Maslov index for
three-dimensional harmonic oscillator is proposed. 相似文献
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To overcome the difficulty of calculating the energy level of quantum harmonic oscillator via traditional method, we derive a new approach by using the normal ordering of the operator and the invariant eigen-operator. Based on this method, we find the energy level of singular harmonic oscillator. 相似文献
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In this paper a new ring-shaped harmonic oscillator for spin 1/2 particles is studied, and the corresponding eigenfunctions and eigenenergies are obtained by solving the Dirac equation with equal mixture of vector and scalar potentials. Several particular cases such as the ring-shaped non-spherical harmonic oscillator, the ring-shaped harmonic oscillator, non-spherical harmonic oscillator, and spherical harmonic oscillator are also discussed. 相似文献
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Bin Kang Cheng 《International Journal of Theoretical Physics》1984,23(12):1099-1104
Horváthy's modification of Feynman's original method is generalized to the path integral formula of a forced harmonic oscillator. With this new formula the propagator of a harmonic oscillator with memory is evaluated exactly beyond and at caustics.Work supported in part by the Conselho Nacional de Desenvolvimento Cientifico e Tecnólogico (CNPq), Brazil. 相似文献
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J.P. Ader 《Physics letters. A》1983,97(5):178-182
A new technique is presented for solving the Schrödinger equation in the framework of the 1/N expansion. Based on recursion relations satisfied by moments of the coordinate operator, this method which allows to compute energy levels and wavefunctions is applied to four examples: the harmonic oscillator, the rotating harmonic oscillator, a linear plus Coulomb potential and a logarithmic one. 相似文献
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In this article, behavioral differences of time-dependent harmonic oscillator in Commutative space and Non-Commutative phase space have been investigated. The considered harmonic oscillator has a time-dependent angular frequency and mass which are function of time. First, the time-dependent harmonic oscillator is studied in commutative space, then similar calculation is done for considered harmonic oscillator in Non-Commutative phase space. During this article method of Lewis–Riesenfeld dynamical invariant has been employed. 相似文献
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In order to extend the conventional shell model (SM) calculation with harmonic oscillator bases to light nuclei on neutron drip line, a self-similar-structure shell model (SSM) is proposed. We do this by a rescaling of both the kinetic and potential energy terms of the harmonic oscillator so that the single-particle orbit in SSM has its own state(orbit)-dependent frequency. Meanwhile, a new method to imitate the Woods-Saxon potential with harmonic oscillator potential is introduced. By the rescaling method and imitation procedure, all light exotic nuclei together with the light stable nuclei are studied in a unified way. The results are in good agreement with experimental data. Furthermore, the puzzle of the unexistence of 5He, 10Li and 13B is naturaUy explained in SSM. 相似文献
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Michał Dobrski 《Central European Journal of Physics》2007,5(3):313-323
In this paper we introduce a method for finding a time independent Hamiltonian of a given Hamiltonian dynamical system by
canonoid transformation of canonical momenta. We find a condition that the system should satisfy to have an equivalent time
independent formulation. We study the example of a damped harmonic oscillator and give the new time independent Hamiltonian
for it, which has the property of tending to the standard Hamiltonian of the harmonic oscillator as damping goes to zero.
相似文献
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OU Yuan-Jin LIANG Xian-Ting 《理论物理通讯》2007,48(5):819-822
In this paper we obtain a propagator of path integral for a harmonic oscillator and a driven harmonic oscillator by using the power series expansion. It is shown that our result for the harmonic oscillator is more exact than the previous one obtained with other approximation methods. By using the same method, we obtain a propagator of path integral for the driven harmonic oscillator, which does not have any exact expansion. The more exact propagators may improve the path integral results for these systems. 相似文献
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M. Boudjema-Bouloudenine T. Boudjedaa A. Makhlouf 《The European Physical Journal C - Particles and Fields》2006,46(3):807-816
We have applied the Schwinger action principle to general one-dimensional (1D), time-dependent quadratic systems via linear
quantum canonical transformations, which allowed us to simplify the problems to be solved by this method. We show that while
using a suitable linear canonical transformation, we can considerably simplify the evaluation of the propagator of the studied
system to that for a free particle. The efficiency and exactness of this method is verified in the case of the simple harmonic
oscillator. This technique enables us to evaluate easily and immediately the propagator in some particular cases such as the
damped harmonic oscillator, the harmonic oscillator with a time-dependent frequency, and the harmonic oscillator with time-dependent
mass and frequency, and in this way the propagator of the forced damped harmonic oscillator is easily calculated without any
approach.
PACS 02.30.Xx, 03.65.-w, 03.65.Ca 相似文献