Orbital angular momentum in phase space

A comprehensive theory of the Weyl–Wigner formalism for the canonical pair angle–angular momentum is presented. Special attention is paid to the problems linked to rotational periodicity and angular-momentum discreteness.     

Inverse problem of mechanics in momentum space

The problem is solved of reproducing a spherically symmetric potential by means of the velocity vector hodograph in a classical mechanics approximation. A definite transcendental equation is obtained for the radial velocity dependence. Considered as an illustration is the problem of the Maxwell fish eye. A relativistic generalization is given. The algorithms constructed can be used to retrieve potentials possessing internal symmetries in the classical or quantum cases.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 46–50, January, 1985.In conclusion, I am grateful to Prof. Yu. N. Demkov for active and stimulating interest in the research.     

The Aharonov-Bohm effect in the momentum space

The Schrödinger formalism of quantum mechanics is used to demonstrate the existence of the Aharonov-Bohm effect in momentum space and set-ups for experimentally demonstrating it are proposed for either free or ballistic electrons.     

Quarkonium bound-state problem in momentum space revisited

A semi-spectral Chebyshev method for solving numerically singular integral equations is presented and applied in the quarkonium bound-state problem in momentum space. The integrals containing both, logarithmic and Cauchy singular kernels, can be evaluated without subtractions by dedicated automatic quadratures. By introducing a Chebyshev mesh and using the Nystrom algorithm the singular integral equation is converted into an algebraic eigenvalue problem that can be solved by standard methods. The proposed scheme is very simple to use, is easy in programming and highly accurate.     

Solution of Coulomb system in momentum space

The solution of D-dimensional Coulomb system is solved in momentum space by path integral. From which the topological effect of a magnetic flux in the system is given. It is revealed that the flux effect represented by the two-dimensional field of Aharonov-Bohm covers any space-dimensions.     

Use of the momentum approximation in classical scattering calculations

Abstract

The validity range of the momentum approximation in binary collisions : s investigated. It is shown that at high energies, E ? 10 · Z ₁ Z ₂ e ²/a _TF, the approximation is even applicable to scattering angles ? as large as 60 degrees. An empirical formula for the evaluation of the momentum approximation employing the Thomas-Fermi-Moliére potential is given. It reduces the computer time to calculate ? to ～⊥₁₀ of the time consumed in using the standard algebraic functions appearing in the momentum approximation.     

Quantum mechanics in discrete space and angular momentum

Recently we have studied quantum mechanics of bounded operators with a discrete spectrum. In particular, we derived an expression for the commutator[Q, P] of two bounded operators whose spectrum is discrete, and we showed that in the limit of a continuous spectrum the commutator becomes the standard one of Heisenberg. In this paper we show that the angular momentum operator and the phase operator satisfy the new commutation relation. We also briefly discuss the problem of the canonical phase operator conjugate to the number operator.     

Hartree-Fock-Slater exchange for anisotropic occupation in momentum space

It is shown that the well-known expression of the Hartree-Fock-Slater exchange energy (usually calculated for an occupied Fermi sphere) becomes scaled by a dimensionless factor in the case of a simple (compact) Fermi body and of only one (partially filled) band. Analytical results are presented for the following occupied regions in momentum space: i) ellipsoid of revolution (prolate as well as oblate), ii) ellipsoid with three unequal axes.The authors would like to thank Prof. P. Ziesche, Dr. H. Eschrig, and Dr. W. John for helpful discussions. One of us (M. H.) acknowledges an IREX-fellowship where part of this work has been completed.     

Solution of Coulomb path integral in momentum space

The path integral for a point particle in a Coulomb potential is solved in momentum space. The solution permits us to answer for the first time an old question of quantum mechanics in curved spaces raised in 1957 by DeWitt: The Hamiltonian of a particle in a curved space must not contain an additional term proportional to the curvature scalar R, since this would change the level spacings in the hydrogen atom.     

Random phase approximation of angular momentum waves in solid Ortho-hydrogen

A short derivation of the Random Phase Approximation of angular momentum waves in solid Ortho-H₂ is presented. Methods and results of papers on the same topic are compared.     

Numerical simulations of strong-field processes in momentum space

The time-dependent Schrodinger equation(TDSE) is usually treated in the real space in the textbook.However,it makes the numerical simulations of strong-field processes difficult due to the wide dispersion and fast oscillation of the electron wave packets under the interaction of intense laser fields.Here we demonstrate that the TDSE can be efficiently solved in the momentum space.The high-order harmonic generation and above-threshold ionization spectra obtained by numerical solutions of TDSE in momentum space agree well with previous studies in real space,but significantly reducing the computation cost.     

Beta decays with momentum space Majorana spinors

We construct and apply to decays a truly neutral local quantum field that is entirely based upon momentum space Majorana spinors. We make the observation that theory with momentum space Majorana spinors of real C parities is equivalent to Diracs theory. For imaginary C parities, the neutrino mass can drop out from the single decay trace and reappear in , a curious and in principle experimentally testable signature for a non-trivial impact of Majorana framework in polarization experiments.Received: 11 November 2003, Revised: 20 April 2004, Published online: 12 October 2004PACS: 11.30.Er Charge conjugation, parity, time reversal, and other discrete symmetries - 14.60.St Non-standard-model neutrinos, right-handed neutrinos, etc.     

在动量空间讨论二氯乙烯的同分异构性

通过量化计算得到了二氯乙烯偏式、顺式和反式三种同分异构体的几何结构参数, 并利用电子动量谱学方法计算了二氯乙烯偏式、顺式和反式同分异构体的四个芯轨道的动量密度二维分布图和动量谱线. 对比不同异构体的四个芯轨道在坐标空间和动量空间的电子分布情况发现, 在坐标空间无法体现的原子轨道间的相互干涉作用在动量空间被放大了, 表现为动量曲线具有多峰结构和一定的周期性. 通过计算周期值可以求出不同异构体相邻原子间的间距; 通过判断周期轴的方向能够得到三种异构体的分子轴取向.     

Threshold resummation in momentum space from effective field theory

Methods from soft-collinear effective theory are used to perform the threshold resummation of Sudakov logarithms for the deep-inelastic structure function F2(x,Q2) in the end-point region x-->1 directly in momentum space. An explicit all-order formula is derived, which expresses the short-distance coefficient function C in the convolution F2 = C multiply sign in circle phi q in terms of Wilson coefficients and anomalous dimensions defined in the effective theory. Contributions associated with the physical scales Q2 and Q2(1-x) are separated from nonperturbative hadronic physics in a transparent way. A crucial ingredient to the momentum-space resummation is the exact solution to the integro-differential evolution equation for the jet function, which is derived. The methods developed in this Letter can be applied to many other hard QCD processes.