共查询到20条相似文献,搜索用时 31 毫秒
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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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提出了一种新的类Quesne环状球谐振子势,应用二分量方法求解1/2-自旋粒子满足的Dirac方程, Dirac哈密顿量由标量和矢量类Quesne环状球谐振子势构成.在Σ=S(r)+V(r)=0的条件下,得到了Dirac旋量波函数下分量的束缚态解和能谱方程, 显示出类Quesne环状球谐振子势场中的赝自旋对称性.讨论了束缚态波函数和能谱方程的有关性质.
关键词:
类Quesne环状球谐振子势
Dirac方程
赝自旋对称性
束缚态 相似文献
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Min-Cang Zhang 《International Journal of Theoretical Physics》2009,48(9):2625-2632
The pseudospin symmetry for a ring-shaped non-spherical harmonic oscillator potential is investigated by solving the Dirac
equation with equal mixture of scalar and vector potentials with opposite signs. The normalized spinor wave function and energy
equation are obtained, the algebraic property of the energy equation and some particular cases are also discussed. 相似文献
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非球谐振子势的精确解 总被引:6,自引:0,他引:6
严格求解了三维非球谐振,势的Schrodinger方程给出了精确的能谱方程和归一化的径向波函数.获得了径向幂次算符rs的矩阵元和平均值的计算公式及其递推关系. 相似文献
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Bound states of Klein-Gordon equation for ring-shaped harmonic oscillator scalar and vector potentials 下载免费PDF全文
Solving Klein-Gordon equation with equal ring-shaped harmonic oscillator scalar and vector potentials, we obtain the exact normalized bound-state wavefunction and energy equation. 相似文献
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Min-Cang Zhang 《Central European Journal of Physics》2009,7(4):768-773
A new double ring-shaped spherical harmonic oscillator potential is presented. The pseudospin symmetry in this system is investigated
by solving the Dirac equation with equal mixture of scalar and vector potentials with opposite signs. The normalized spinor
wave function and energy equation are obtained and some particular cases are discussed.
相似文献
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We show that the exact energy eigenvalues and eigenfunctions of the Schrödinger equation for charged particles moving in certain class of non-central potentials can be easily calculated analytically in a simple and elegant manner by using Nikiforov and Uvarov (NU) method. We discuss the generalized Coulomb and harmonic oscillator systems. We study the Hartmann Coulomb and the ring-shaped and compound Coulomb plus Aharanov–Bohm potentials as special cases. The results are in exact agreement with other methods. 相似文献
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Bound states of Klein—Gordon equation for double ring-shaped oscillator scalar and vector potentials 总被引:1,自引:0,他引:1 下载免费PDF全文
In spherical polar coordinates, double ring-shaped oscillator potentials have supersymmetry and shape invariance for θ and r coordinates. Exact bound state solutions of Klein—Gordon equation with equal double ring-shaped oscillator scalar and vector potentials are obtained. The normalized angular wavefunction expressed in terms of Jacobi polynomials and the normalized radial wavefunction expressed in terms of the Laguerre polynomials are presented. Energy spectrum equations are obtained. 相似文献
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Ali Ghoumaid Farid Benamira Larbi Guechi Zohra Khiat 《Central European Journal of Physics》2013,11(1):78-88
We present a rigorous path integral treatment of a dynamical system in the axially symmetric potential $V(r,\theta ) = V(r) + \tfrac{1} {{r^2 }}V(\theta ) $ . It is shown that the Green’s function can be calculated in spherical coordinate system for $V(\theta ) = \frac{{\hbar ^2 }} {{2\mu }}\frac{{\gamma + \beta \sin ^2 \theta + \alpha \sin ^4 \theta }} {{\sin ^2 \theta \cos ^2 \theta }} $ . As an illustration, we have chosen the example of a spherical harmonic oscillator and also the Coulomb potential for the radial dependence of this noncentral potential. The ring-shaped oscillator and the Hartmann ring-shaped potential are considered as particular cases. When α = β = γ = 0, the discrete energy spectrum, the normalized wave function of the spherical oscillator and the Coulomb potential of a hydrogen-like ion, for a state of orbital quantum number l ≥ 0, are recovered. 相似文献
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The notion of wave function of the classical harmonic oscillator is discussed. The evolution equation for this wave function
is obtained using the classical Liouville equation for the probability-distribution function of the harmonic oscillator. The
tomographic-probability distribution of the classical oscillator is studied. Examples of the ground-like state and the coherent
state of the classical harmonic oscillator are considered. 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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Exact solutions of the Klein—Gordon equation with ring-shaped oscillator potential by using the Laplace integral transform 下载免费PDF全文
Sami Ortakaya 《中国物理 B》2012,21(7):70303-070303
We present exact solutions for the Klein-Gordon equation with a ring-shaped oscillator potential. The energy eigenvalues and the normalized wave functions are obtained for a particle in the presence of non-central oscillator potential. The angular functions are expressed in terms of the hypergeometric functions. The radial eigenfunctions have been obtained by using the Laplace integral transform. By means of the Laplace transform method, which is efficient and simple, the radial Klein-Gordon equation is reduced to a first-order differential equation. 相似文献
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二维各向同性变频率谐振子的超对称性及其不变量的超对称量子力学精确解 总被引:1,自引:0,他引:1
采用超对称量子力学与不变量相结合的方法讨论了二维各向同性变频率谐振子,给出了二维各向同性变频率谐振子的不变量,采用超对称量子力学方法精确求解了不变量的本征值和本征函数,并且给出了当频率恒定时,二维常频率谐振子的本征值和本征函数的精确解.最后对不变量的超对称性进行了讨论. 相似文献
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Jeong-Ryeol Choi 《Reports on Mathematical Physics》2003,52(3):321-329
Exact solution of the Schrödinger equation is derived for underdamped, critically damped, and overdamped harmonic oscillators with a driving force. A unitary operator transforming Hamiltonian into a simple form is introduced. The transformed Hamiltonian, represented in terms of a modified frequency ω, is identical with the Hamiltonian of the standard harmonic oscillator for the underdamped oscillator, with the Hamiltonian of a free particle for the critically damped oscillator, and with the Hamiltonian of a system with a harmonic parabolic potential for the overdamped oscillator. The eigenvalues of underdamped oscillator are discrete while those of the critically damped and the overdamped oscillators are continuous. 相似文献