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一维无限深方势阱模型是量子力学理想模型,经典教材中势阱的边界一般取得比较特殊.或关于坐标原点具有对称性,或势阱左边界位于坐标原点.本文首先展示了如何利用3种方法求解一维任意边界无限深方势阱能量本征值和对应的本征态,不同方法得到的结果彼此之间等价,讨论分析了这3种方法的推导结果,然后得到关于一维任意边界无限深方势阱能量本征值和本征态的通式,从中比较容易看出这两个物理量均与阱宽有关,并且本征波函数与边界值有关,最后将一维结果拓展到二维和三维任意边界无限深方势阱情况. 相似文献
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介绍了用α0迭代方法求一维有限深方势阱的解析近似解,给出了解的通式和可求任意精度要求解的α0循环迭代计算程序流程。在新的基础上建立有限深方势阱的能级和波函数与无限深方势阱的能级和波函数的联系。 相似文献
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对有限深方势阱中的能级方程做一个简单的数学变换,从而将常用的图解法中的函数图像简化,使得有限深方势阱问题的物理图像变得更清晰,更有利于大家理解这个简单而重要的模型.文中还利用改进后的图解法简单讨论了一些有限深方势阱的性质. 相似文献
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在一维问题的基础上探讨了二维无限深势阱的问题,发掘二维无限深势阱在不同边界约束情况下不同于一维问题的特征和应用. 相似文献
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主要对量子力学一维有限深方势阱中运动粒子的束缚态存在条件进行讨论.通过求解定态薛定谔方程,得到粒子运动满足的超越方程,借助于Mathematica软件求解该超越方程得到粒子的能级结构,对粒子束缚态存在条件进行分析.结果表明,对于在一维有限深对称方势阱中运动的粒子,总会有束缚态的存在,和势阱的宽度、深度及粒子的质量无关.而在半壁有限深势阱中运动的粒子,出现束缚态是有条件的.并且分别给出了在两种势阱中粒子存在多个束缚态需要满足的条件. 相似文献
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Claudio Albanese 《Communications in Mathematical Physics》1988,120(1):97-103
We consider the Hartree equations for a system of an infinite number of electrons in a periodic potential consisting of a periodic array of wells. The filling fraction is assumed to be of one electron per well. We prove that if the wells are deep enough to admit a bound state and if they are separated by a distance large enough, then the Hartree equations have a solution in which all single particle wave functions decay exponentially. 相似文献
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Two simple dynamic systems with cubic nonlinearity and additive Gaussian white noise are used to assess the performance and the usefulness of closure methods in nonlinear random vibration. One of the systems has a single potential well while the other has two potential wells. It is shown that the performance of closure methods is determined by the structure of the moment equations rather than the way in which these equations are closed. For the system with one potential well, any closure method is satisfactory. For the system with two potential wells, closure methods can be inaccurate irrespective of the closure level. It is also shown that moment equations can be augmented with moment inequalities to solve approximately the infinite hierarchy of moment equations. 相似文献
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N. E. Ainbinder G. E. Kibrik A. N. Osipenko G. B. Soifer 《Physics of the Solid State》1997,39(5):780-782
This paper presents the results of an experimental and theoretical study of reorientational molecular motion between unequal
potential wells in a three-well potential bounded by infinite walls. The temperature dependences of the nuclear spin-lattice
relaxation times in crystalline pentafluorochlorobenzene, C6F5Cl, (magnetic for fluorine 19 and quadrupole for chlorine 35) have been analyzed on the basis of the theoretical expressions
obtained here. The parameters of the orientational potential with unequal wells have been established as a result of this
interpretation of the experimental data.
Fiz. Tverd. Tela (St. Petersburg) 39, 877–879 (May 1997) 相似文献
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The dynamics of a particle interacting with a random classical field in a two-well potential is studied by the functional integration method. The probability of particle localization in either of the wells is studied in detail. Certain field-averaged correlation functions for quantum-mechanical probabilities and the distribution function for the probabilities of final states (which can be considered as random variables in the presence of a random field) are calculated. The calculated correlators are used to discuss the dependence of the final state on the initial state. One of the main results of this work is that, although the off-diagonal elements of the density matrix disappear with time, a particle in the system is localized incompletely (wave-packet reduction does not occur), and the distribution function for the probability of finding particle in one of the wells is a constant at infinite time. 相似文献
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《Infrared physics》1990,30(4):363-370
We have evaluated the energy levels of a particle in an infinite potential well containing identical square-potential barriers of equal width and separation, in a symmetric as well as an asymmetric arrangement, as functions of the number and height of the potential barriers. For this purpose we have derived analytical equations for the energy eigenvalues which can be solved with a personal computer. We show plots of the normalized energy levels of particles in potential wells containing up to three identical square-potential barriers with heights varying from zero to infinity. These can be applied to models of inversion and libration of molecules, electronic states in dye molecules, quantum well structures, etc. 相似文献
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In this study, the effects of quantum confinement and effective mass anisotropy parameter on the diamagnetic susceptibility of a hydrogenic donor placed in GaAs, Si, and Ge quantum wells with infinite confinement potential are investigated in the effective mass and parabolic band approximations by using two and one parameter trial wave functions. It is observed that the diamagnetic susceptibility of a hydrogenic donor in anisotropic quantum wells is essentially equal to the transverse diamagnetic susceptibility part when well widths are larger than L > 100 Å, and the impurity is located at center. Moreover, a two parameter trial wave function model gives higher values of diamagnetic susceptibility, except for χz (GaAs). 相似文献
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The acceleration theorem of Bloch waves is utilized to construct random potential wells for classical acoustic waves in systems composed of alternating‘cavities’and‘couplers’.One prominent advantage of this method is these‘cavities’and‘couplers’are all monolayer structures.It allows forming more compact classical potential wells,which leads to the miniaturization of acoustic devices.We systematically investigate properties of harmonic,tangent,hyperbolic function,and square classical potential wells in quasi-periodic superlattices.Results show these classical potential wells are analogues of quantum potential wells.Thus some technologies and concepts in quantum potential well fields may be generalized to classical acoustic wave fields.In addition,some abnormal cases regarding forming classical potential wells are also found. 相似文献
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抛物量子阱中束缚极化子的极化势和结合能 总被引:3,自引:1,他引:2
利用改进的Lee-Low-Pines(LLP)方法,用变分法计算了无限深抛物量子阱中同时考虑与体纵光学声子和界面纵光学声子相互作用的束缚极化子的极化势和结合能.数值计算得出:阱宽较大时极化势很小,阱宽较小时极化势较大,所以对于较窄的抛物阱必须考虑极化势.对于给定阱宽的抛物阱,随着远离阱中心极化势迅速减小,当到达阱的界面附近极化势又开始增大.阱宽较小时,束缚极化子的结合能随着阱宽L的增大而急剧减小;阱宽较大时,结合能减小的非常缓慢,最后接近体材料中的三维值. 相似文献
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G. Foffi E. Zaccarelli F. Sciortino P. Tartaglia K. A. Dawson 《Journal of statistical physics》2000,100(1-2):363-376
We discuss the situation where attractive and repulsive portions of the interparticle potential both contribute significantly to glass formation. We introduce the square-well potential as prototypical model for this situation, and reject the Baxter model as a useful model for comparison to experiment on glasses, based on our treatment within mode coupling theory. We present explicit results for various well widths, and show that, for narrow wells, there is a useful analytical formula that would be suitable for experimentalists working in the field of colloidal science. We raise the question as to whether, in a more exact treatment, the sticky-sphere limit might have an infinite glass transition temperature or a high but finite one. 相似文献
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We study the energy band structure of magnetic graphene superlattices with delta-function magnetic barriers and zero average magnetic field. The dispersion relation obtained using the T-matrix approach shows the emergence of an infinite number of Dirac-like points at finite energies, while the original Dirac point is still located at the same place as that for pristine graphene. The carrier group velocity at the original Dirac point is isotropically renormalized, but at finite energy Dirac points it is generally anisotropic. An asymmetry in the width between the wells and the barriers of the periodic potential induces a shift of the original Dirac point in the zero-energy plane, keeping the velocity renormalization isotropic. 相似文献