The 4D Klein-Gordon, Dirac and Quantization Equations from 5D Null Paths

Results from 5D induced-matter and membrane theory with null paths are extended to show that a particle obeys the 4D Klein-Gordon equation but with a variable mass. The Dirac equation also follows, but raises concerns about 4D quantization in the two natural 5D gauges, and reopens the question of a Regge-like trajectory for the spin angular momenta and squared masses of gravitationally-dominated systems.     

相对论性无自旋粒子在Hartmann势场中运动的精确解

在标量势等于矢量势的条件下,本文获得了具有Hartmann型势的Klein-Gordon方程的精确解.给出了束缚态的精确的能谱方程和归一化的径向波函数,对于散射态,获得了按“k/2π标度”归一化的径向波函数和相移的解析计算公式.讨论了散射振幅的解析性质和波函数、能谱方程以及相移的非相对论近似.     

Classical limit of relativistic quantal system with attractive Coulomb interaction

Using the appropriate harmonic oscillator states and reasonable approximations, we construct coherent wavepackets corresponding to the solutions of the Klein-Gordon equation for the attractive potentialV(r)=−k/r, k>0, in two and three space dimensions. We deduce the corresponding classical limit in two dimension by requiring that the expectation value 〈r〉 of the radial variable is large. In the case of three dimensions, besides the condition of large 〈r〉, we make the uncertainty Δr=[〈r ²〉 − 〈r〉²]^1/2 a minimum with respect to certain parameter of the wavepacket. We then investigate the trajectory traversed by the wavepacket in the classical limit. We find that the classical limit of this relativistic quantal problem gives, in the leading order, the same expression for the rate of motion of the perihelion as that given by the solution of the corresponding special relativistic classical dynamical problem. We also briefly discuss some of the subtle aspects of the classical limit of the relativistic quantal system, in general.     

GLOBAL WEAK SOLUTIONS OF THE RELATIVISTIC VLASOV-KLEIN-GORDON SYSTEM IN TWO DIMENSIONS

In this paper we consider the system of classical particles coupled with a Klein-Gordon field in two dimensions.We establish a-priori-bounds on the solutions of this system with initial data satisfying a size restriction derived from conservation of energy.This result,together with the smoothing of"velocity averaging",yields the existence of global weak solutions to the corresponding restricted initial value problem.The size restriction is necessary since energy of the system is indefinite.Finally,we show that the weak solutions preserve the total mass.     

Pion absorption by16O using realistic interactions—II: Free pion absorption followed by emission of proton

Matrix element of the Gallilean invariant nonrelativistic reduction of the pseudoscalar-pseudovector interaction has been calculated for free pion absorption by a single nucleon inside the nucleus of¹⁶O. The Hartree-Fock wavefunctions obtained with the unitary-model-operator approach starting with the hard-core nucleon-nucleon interaction have been used for the π-capturing nucleon in the initial state. The initial pion distortion in the presence of nuclear field of the absorbing nucleus prior to its absorption together with the Coulomb interaction with the finite nuclear size has been taken into account. The distortion of the emitted proton in the field of the residual nucleus has also been considered. The differential cross-sections have been obtained and calculated results are compared with the previous experimental and theoretical work.     

Solvable relativistic quantum dots with vibrational spectra

For Klein-Gordon equation a consistent physical interpretation of wave functions is reviewed as based on a proper modification of the scalar product in Hilbert space. Bound states are then studied in a deep-square-well model where the spectrum is roughly equidistant and where a fine-tuning of the levels is mediated by -symmetric interactions (composed of imaginary delta functions) which mimic creation/annihilation processes. Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.     

相对论情况下赝自旋对称性势场中运动粒子的束缚态

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.     

Bound-State Solutions of the Klein-Gordon Equation for the Generalized <Emphasis Type="Italic">PT</Emphasis>-Symmetric Hulthén Potential

The one-dimensional Klein-Gordon equation is solved for the PT-symmetric generalized Hulthén potential in the scalar coupling scheme. The relativistic bound-state energy spectrum and the corresponding wave functions are obtained by using the Nikiforov-Uvarov method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type. PACS numbers: 03.65.Fd, 03.65.Ge     

On dispersive properties of discrete 2D Schrödinger and Klein-Gordon equations

We derive the long-time asymptotics for solutions of the discrete 2D Schrödinger and Klein-Gordon equations.     

Hamilton operator and the semiclassical limit for scalar particles in an electromagnetic field

We successively apply the generalized Case-Foldy-Feshbach-Villars (CFFV) and the Foldy-Wouthuysen (FW) transformation to derive the Hamiltonian for relativistic scalar particles in an electromagnetic field. In contrast to the original transformation, the generalized CFFV transformation contains an arbitrary parameter and can be performed for massless particles, which allows solving the problem of massless particles in an electromagnetic field. We show that the form of the Hamiltonian in the FW representation is independent of the arbitrarily chosen parameter. Compared with the classical Hamiltonian for point particles, this Hamiltonian contains quantum terms characterizing the quadrupole coupling of moving particles to the electric field and the electric and mixed polarizabilities. We obtain the quantum mechanical and semiclassical equations of motion of massive and massless particles in an electromagnetic field. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 3, pp. 398–411, September, 2008.