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求解了非球谐振子势场中1/2自旋粒子满足的Dirac方程,Dirac哈密顿量包含有标量非球谐振子势S(r)和矢量非球谐振子势V(r).在Σ(r)=S(r)+V(r)=0和Δ(r)=V(r)-S(r)=0的条件下,解析地得到了Dirac旋量波函数的束缚态解和能谱方程,结果表明非球谐振子势
关键词:
非球谐振子势
Dirac方程
赝自旋对称性
束缚态 相似文献
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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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提出了一种新的精确可解的三维解析势函数,即环形非球谐振子。势函数为V(γ,θ)=1/2mω^2γ^2 h^2/2mA/γ^2 h^2/2mb/γ^2sin^2θ。将环形非球谐振子势的Schroedinger方程在球坐标系中进行变量分离,得到了角向方程和径向方程,给出了精确的能谱方程,获得了用普遍的associated-Legendre多项式表示的归一化的角向波函数和用合流超几何函数表示的归一化的径向波函数。球谐振子、非球谐振子和环形振子的有关结果均作为特例包含在本文的一般结论之中。 相似文献
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讨论了3种变形谐振子势:左右两边不同参数的谐振子势、左边方形势加右边谐振子势和谐振子势中间加δ势中的能量本征态函数.这些函数都可以由厄米函数表示.由波函数及其一次导数在原点的衔接条件,得到了能谱方程. 相似文献
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The periodic motion of the classical anharmonic oscillator characterized by the potentialV(x)=1/2x
2+λ/2k x
2k
is considered. The period is first determined to all orders inλ in a perturbative series. Making use of this, the solution of the nonlinear equation of motion is then expressed in the form
of a Fourier series. The Fourier coefficients are obtained by solving simple algebraic relations. Secular terms are inherently
absent in this perturbative scheme. Explicit solution is presented for generalk up to the second order, from which the Duffing and the sextic oscillator results follow as special cases. 相似文献
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Martin Schwarz Jr. 《Journal of statistical physics》1976,15(3):255-261
In the present study we investigate the statistical thermodynamics of the anharmonic oscillator, whose energies are characterized by the potential 1/2x
2+x
4. Employing the energies recently obtained by Hioe and Montroll, we compute the partition function and the thermodynamic quantities for the anharmonic and quartic oscillators. Low- and high-temperature formulas are presented for the thermodynamic quantities of the oscillators. 相似文献
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S. K. Bose 《Letters in Mathematical Physics》1979,3(4):259-264
We obtain here a perturbative solution of the generalx
2q+2
anharmonic damped oscillator in the coherent state representation. The solution does not contain any secular term and shows, explicitly, the damping and the anharmonic effects. 相似文献
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We obtain sufficiently accurate eigenvalues and eigenfunctions for the anharmonic oscillator with potential V(x, y) = x 2 y 2 by means of three different methods. Our results strongly suggest that the spectrum of this oscillator is discrete in agreement with early rigorous mathematical proofs and against a recent statement that cast doubts about it 相似文献
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W. K. McClary 《Communications in Mathematical Physics》1972,24(3):171-179
A class of perturbation problems is considered, in which the Rayleigh-Schrödinger perturbation series for the ground state eigenvalue and eigenvector are presumed to diverge. This class includes the (:2m
:g(x))2, (m=2, 3) quantum field theory models and the quantum mechanical anharmonic oscillator. It is shown that, using matrix elements and vectors which occur in the series coefficients, one may construct convergent approximants to the eigenvalue and eigenvector. Results of a calculation of the ground state energy of thex
4 anharmonic oscillator are given.Supported in part by the National Research Council of Canada. 相似文献
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We obtain exact solutions for the motion of a classical anharmonic oscillator in the potential Bx
2–|A|x
4+Cx
6, and discuss the energy dependence of the frequencies of oscillation. 相似文献
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S. Brajamani P. S. Mazumdar S. K. Chowdhury Sukanya Sur 《International Journal of Theoretical Physics》1991,30(4):487-493
The ground state and first few excited energy levels of the generalized anharmonic oscillator defined by the HamiltonianH=–d
2/dx
2+x
2+x
2k (k=3, 4,...) have been calculated by employing the method of quantum normal form, which is the quantum mechanical analogue of the classical Birkhoff-Gustavson normal form. The present energy eigenvalues are consistent with other tabulations of the energy levels. 相似文献
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Nazakat Ullah 《Pramana》1985,24(1-2):27-29
The linearization technique of random phase approximation is applied to the anharmonic oscillator to find a modified perturbation
series. It is shown that for the anharmonic termλx
4, the ground state energyE
0 upto the second order of perturbation is given byE
0=(35/48) (3/4)1/3
λ
1/3 asλ→∞. 相似文献
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We study the ground state as well as the first three excited states of the anharmonic oscillator with anharmonicity λx4 for a range of λ = (0, 10) with the first-order logarithmic perturbation iteration method (FOLPIM). This leads to convergent results. The initial choice of the wave function seems only to affect the rate of convergence in the case of the ground state but may critically affect the convergence for the excited states. For large values of λ, convergence is best obtained by choosing the asymptotic solution as the initial “unperturbed” wave function. 相似文献
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本文利用接合法,研究了具有Goodwin特性的Le Corbeiller二拍振荡器模型。并由点变换及后继函数的理论,找到了这个系统具有周期解,且解为唯一的及稳定的条件。给出了周期解的波形及周期的表达式。 相似文献