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1.
根据Heisenberg对应原理(HCP),在经典极限下厄密算符的量子矩阵元对应经典物理量的Fourier展开系数.将HCP应用到相对论领域的Dirac方程中,对于自由粒子和在匀磁场中的带电粒子,其量子算符的矩阵元在经典极限下对应着相对论物理方程的解.计算表明,在经典极限下量子期望值就是对应经典物理量的时间平均值. 相似文献
2.
在赝自旋对称性条件下,分别求解了在M rse型和Tan2(πηr)型标量势与矢量势场中运动的相对论粒子的Klein-Gordon方程和Dirac方程,给出了它们的束缚态能谱和相对论性波函数. 相似文献
3.
伪自旋对称情形下Rosen-Morse类型势场中相对论粒子的束缚态 总被引:1,自引:1,他引:0
在伪自旋对称情形下研究了Rosen-Morse类型势场中相对论粒子的束缚态,利用Nikiforov-Uvarov方法求解了伪自旋对称情形下的Klein-Gordon和Dirac方程,得到了相对论粒子被束缚在Rosen-Morse类型势场的精确束缚态解. 相似文献
4.
给出了具有Rosen-Morse型标量势与矢量势的Klein-Gordon方程和Dirac方程的s波束缚态解. 运用超对称量子力学和形不变性得到了束缚态能谱,通过变量代换求得波函数. 把上述方法推广到相对论量子力学.
关键词:
Rosen-Morse势
Klein-Gordon方程
Dirac方程
束缚态 相似文献
5.
在赝自旋对称性势场中运动的相对论粒子的束缚态 总被引:1,自引:1,他引:0
在赝自旋对称性条件下,分别求解了在Kratzer型、Hulthén型和Poschl-Teller型标量势与矢量势场中运动的相对论粒子的Klein-Gordon方程和Dirac方程,给出了它们的束缚态能谱和相对论性波函数. 相似文献
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给出了具有tan2(πηr)型标量势和矢量势的KleinGordon方程和Dirac方程的s波束缚态解,并与无限深球方势阱的情况进行了比较.
关键词:
tan~2(πηr)势
KleinGordon方程
Dirac方程
束缚态 相似文献
11.
Quantum matrix elements of the coordinate, momentum and the velocity operator for a spin-1/2 particle moving in a scalar-like
potential are calculated. In the large quantum number limit, these matrix elements give classical quantities for a relativistic
system with a position-dependent mass. Meanwhile, the Klein-Gordon equation for the spin-0 particle is discussed too. Though
the Heisenberg equations for both the spin-0 and spin-1/2 particles are unlike the classical equations of motion, they go
to the classical equations in the classical limit.
相似文献
12.
This work provides an accurate study of the spin-l/2 relativistic particle in a magnetic field in NC phase space. By detailed calculation we find that the Dirac equation of the relativistic particle in a magnetic field in noncommutative space has similar behaviour to what happens in the Landau problem in commutative space even if an exact map does not exist. By solving the Dirac equation in NC phase space, we not only obtain the energy level of the spin-1/2 relativistic particle in a magnetic field in NC phase space but also explicitly offer some additional terms related to the momentum-momentum non-commutativity. 相似文献
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This work provides an accurate study of the spin-1/2 relativistic particle in a magnetic field in NC phase space. By detailed calculation we find that the Dirac equation of the relativistic particle in a magnetic field in noncommutative space has similar behaviour to what happens in the Landau problem in commutative space even if an exact map does not exist. By solving the Dirac equation in NC phase space, we not only obtain the energy level of the spin-1/2 relativistic particle in a magnetic field in NC phase space but also explicitly offer some additional terms related to the momentum-momentum non-commutativity. 相似文献
15.
This paper provides a study of Wigner functions for a spin-1/2 relativistic particle in the presence of magnetic field. Since
the Dirac equation is described as a matrix equation, it is necessary to describe the Wigner function as a matrix function
in phase space. What’s more, this function is then proved to satisfy the Dirac equation with ⋆-product. Finally, by solving
the ⋆-product Dirac equation, the energy levels as well as the Wigner functions for a spin-1/2 relativistic particle in the
presence of magnetic field are obtained. 相似文献
16.
According to the Heisenberg correspondence principle, in the classical limit, quantum matrix element of a Hermitian operator reduces to the coefficient of the Fourier expansion of the corresponding classical quantity. In this article, such a quantum-classical connection is generalized to the relativistic regime. For the relativistic free particle or the charged particle moving in a constant magnetic field, it is shown that matrix elements of quantum operators go to quantities in Einstein’s special relativity in the classical limit. Especially, matrix element of the standard velocity operator in the Dirac theory reduces to the classical velocity. Meanwhile, it is shown that the classical limit of quantum expectation value is the time average of the classical variable. 相似文献
17.
在本文中,作者推得一组相对论式的汉密尔敦运动式;并根据此运动式,详细地讨论了一质点之运动;由此还可以很自然地看出,在量子力学中,狄拉克电子方程式似乎是一个必然的波动方程式。在狄拉克理论中的取平方根步骤在这里找到它在古典物理学中的对照。同时根据了上面的理论,作者还推得到一个相对论式的哈生堡方程式,最后则讨论了此方程式在狄拉克电子理论中的一些应用;同时并指出,在相对论的观点上,此方程式可以引导出一些比较对称的及有比较普遍形式的物理的量。 相似文献
18.
We investigate the decay of initial correlations in a spin system where each spin relaxes independently by an intramolecular mechanism. The equation of motion for the spin density matrix is assumed to be the Redfield equation, which is of the form of a quantum mechanical master equation. Our analysis of this problem is based on the techniques of Shuler, Oppenheim, and coworkers, who have studied the decay of correlations in systems which can be described by classical stochastic master equations. We find that the off-diagonal elements of the reduced spin density matrices approach their equilibrium values faster than the diagonal elements. The Ursell functions, which are a measure of the correlations in the system, decay to their zero equilibrium values faster than the spin density matrix except for the furthest off-diagonal elements. Far off-diagonal matrix elements of the spin density matrix approach equilibrium at the same rate as the Ursell functions, which is the important difference between the quantum mechanical model studied here and the classical models studied earlier.Supported in part by the National Science Foundation. 相似文献
19.
The Feshbach–Villars equations, like the Klein–Gordon equation, are relativistic quantum mechanical equations for spin-0 particles.We write the Feshbach–Villars equations into an integral equation form and solve them by applying the Coulomb–Sturmian potential separable expansion method. We consider boundstate problems in a Coulomb plus short range potential. The corresponding Feshbach–Villars CoulombGreen’s operator is represented by a matrix continued fraction. 相似文献
20.
Zhenglu Jiang 《Journal of statistical physics》2008,130(3):535-544
By combining the DiPerna and Lions techniques for the nonrelativistic Boltzmann equation and the Dudyński and Ekiel-Jeżewska
device of the causality of the relativistic Boltzmann equation, it is shown that there exists a global mild solution to the
Cauchy problem for the relativistic Boltzmann equation with the assumptions of the relativistic scattering cross section including
some relativistic hard interactions and the initial data satisfying finite mass, energy and entropy. This is in fact an extension
of the result of Dudyński and Ekiel-Jeżewska to the case of the relativistic Boltzmann equation with hard interactions.
This work was supported by NSFC 10271121 and the Scientific Research Foundation for the Returned Overseas Chinese Scholars,
the Ministry of Education of China, and sponsored by joint grants of NSFC 10511120278/10611120371 and RFBR 04-02-39026. 相似文献