The three-body problem in the path integral formalism

The propagator related to the Calogero potential is calculated in the phase space by way of Feynman formalism. The energy spectrum is determined along with the corresponding wave functions. In case some constraints are introduced, the problem may be reduced to the one corresponding to a particle constrained to move into a sector of opening angle α. It is shown as well that complicated potentials, may be transformed to allow the calculation of the energy spectrum via the Kleinert method.     

Boundary conditions in the framework of the path integral formalism

In this paper we propose a modification of the relationship between a short-time propagator and a corresponding classical lagrangian. This modification enables us, in a simple way, to construct path integrals for configuration spaces with boundaries where we have to take into account boundary conditions imposed on the propagator. Simple examples are added as illustrations.     

Fragmentation function in non-equilibrium QCD using closed-time path integral formalism

In this paper we implement the Schwinger–Keldysh closed-time path integral formalism in non-equilibrium QCD in accordance to the definition of the Collins–Soper fragmentation function. We consider a high-p _T parton in QCD medium at initial time τ ₀ with an arbitrary non-equilibrium (non-isotropic) distribution function fragmenting to a hadron. We formulate the parton-to-hadron fragmentation function in non-equilibrium QCD in the light-cone quantization formalism. It may be possible to include final-state interactions with the medium via a modification of the Wilson lines in this definition of the non-equilibrium fragmentation function. This may be relevant to the study of hadron production from a quark–gluon plasma at RHIC and LHC.     

Relationship of effective wave functions and the density matrix formalism

We investigate the relationship between the density matrix formalism and the method of describing quantum systems with wave functions pre-averaged over the thermostat states. It is shown that when fluctuations of the perturbation operator have a duration less than that of the characteristic times of variation of the isolated subsystem and the density matrix of the entire system can be represented as a direct product of the density matrix of the subsystem and the density matrix of the surrounding medium, both approaches lead to Neumann equations of the same structure. Omsk State Technical University. Translated fromIzvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 64–68, July, 1998.     

Electron wave packets: Quantum statistics in path integral representation

Fundamental relations between ensemble-averaged kinetic energy, pressure, and virial are obtained for quantum many-particle systems at finite temperatures. A path-integral method is developed for calculating kinetic energy for mixed (quantum-classical) systems. The method eliminates the problem of divergent variance. Path-integral Monte Carlo simulations are performed to validate the method as applied to single-electron and electron-pair wave packets, with exact treatment of exchange symmetry and spin states. Quantitative results are compared with corresponding characteristics calculated for point charges.     

Electron spectrum and wave functions of icosahedral quasicrystals

Electron spectra and wave functions of icosahedral quasicrystals have been investigated in the tight-binding approximation using the two-fragment structural model (the Amman-MacKay network) with “central” decoration. A quasicrystal has been considered as a limiting structure in a set of optimal cubic approximants with increasing lattice constants. The method of level statistics indicates that the energy spectrum of an icosahedral quasicrystal contains a singular (nonsmooth) component. The density of electron states has been calculated for the first four optimal cubic approximants of the icosahedral quasicrystal, and the respective Lebesgue measures of energy spectra of these approximants have been obtained. Unlike the case of a one-dimensional quasiperiodic structure, the energy spectrum of an icosahedral quasicrystal does not contain a hierarchical gap structure typical of the Cantor set of measure zero in a one-dimensional quasicrystal. Localization of wave functions in an icosahedral quasicrystal has been studied, and their “critical” behavior has been detected. The effect of disorder due to substitutional impurities on electron properties of icosahedral quasicrystals has been investigated. This disorder makes the electron spectrum “smoother” and leads to a tendency to localization of wave functions. Zh. éksp. Teor. Fiz. 113, 1009–1025 (March 1998)     

Radial wave functions of a discrete spectrum

The system of equations for radial wave functions is written in a form allowing both relativistic and non relativistic wave functions to be obtained. In the case of a discrete spectrum, an asymptotic solution of this system is obtained for a potential which includes not only a Coulomb term but also terms corresponding to dipole and quadrupole polarization. The normalizing factor of the asymptote is determined in the approximation of the relativistic quantum-defect method, which offers the possibility, in principle, of using the functions in semiempirical calculations analogous to nonrelativistic calculations by the Bates — Damgaard — Seaton method. The calculation scheme is illustrated for the example of the calculation of Si IV wave functions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 39–44, December, 1978.     

A simple derivation of the WKB energy levels via the path integral

It is pointed out that the leading singularity of e^?βH at β = 0 comes from just the zero frequency mode in the path integral. The WKB energy levels and corrections to it can therefore easily be estimated. However, the method works only for potentials unbounded at infinity.     

Jost functions in the two-potential formalism

For two inhomogeneous Schrödinger equations playing an important role within the framework of the Gell-Mann — Goldberger two-potential formalism we derive the integral equations for the off-shell solutions and give the relations between the regular and Jost solutions. We define the Jost functions fully off the energy shell. The obtained formulae give the possibility to extend the validity of various useful relations derived within the one-potential theory.     

Effects of the overlap between wave functions of impurity centers on the activation energy of hopping conduction

The hopping conductivity σ₃ has been studied in samples of slightly counterdoped crystalline Si: B with a boron concentration of 2×10¹⁶ cm^?3<N<10¹⁷ cm^?3 and a compensation of 10^?4≤K≤10^?2. It is found that at K≤10^?3 the activation energy ε₃ is not lower (as it must be according to classical notions at finite K) but larger than the value ε_N=e ² N ^1/3/κ, where e is the electronic charge and κ is the dielectric constant. With decreasing N, the energy ε₃ drops slower and, with decreasing K, grows faster than follows from the standard theory. At K≤10^?4, ε₃ is higher than ε _N by a factor of 1.5–2. The result is explained by the effect of the overlap between wave functions of neighboring impurity centers on the structure of the impurity band.     

Ground state wave functions in the hyperspherical formalism for nuclei with A>4

The general formulation of a technically advantageous method to find the ground state solution of the Schrödinger equation in configuration space for systems with a number of particles A greater than 4 is presented. The wave function is expanded in pair-correlated hyperspherical harmonics beyond the lowest order approximation and then calculated in the Faddeev approach. A recent efficient recursive method to construct antisymmetric A-particle hyperspherical harmonics is used. The accuracy is tested for the bound state energies of nuclei with A = 6–12. The high quality of the obtained results becomes evident from a comparison with other approaches.     

Variational path integral approach to the ground state energy of artificial atoms

Artificial atoms in different confinement potentials are studied using the Jensen–Feynman variational approach. The density and pair correlation function of an harmonic model with statistics are analytically calculated and used to find the variational ground state energy in two and three dimensions. The results are compared with the numerical calculations and a good correlation is found.     

Minimax-entropy method in estimation of energy spectrum from integral sampled data

The minimax-entropy method is compared with the known nontraditional methods of spectral estimation from a finite set of sample correlation coefficients.Nizhny Novgorod Polytechnic Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 2, pp. 220–225, February, 1994.     

Approximate formulae for the overlap integral of two harmonic oscillator wave functions

The use of second-order perturbation theory to derive approximate formulae for the overlap integral of two harmonic oscillator wave functions is discussed, and the results applied to the theory of intensity distributions in vibrational progressions in electronic spectra. For the vibrational progression m←0 an approximate formula is given which, when the vibrational frequencies of the initial and final states differ by less than 10%, reproduces to an accuracy of 1% or less the intensity profile calculated using the exact formulae for the overlap integrals.     

费米共振对分子振动能级和光谱的影响

费米共振相互作用对多原子分子具有相同对称类的近简并振动能级及其光谱产生影响,利用定态微扰理论,分析了五阶近似下费米共振对三个振动能级的影响,应用于CO2分子的(0400),(1200)和(2000)三个近简并能级,计算结果与实验观测值符合较好,并讨论了费米共振对(0400),(1200)和(2000)向(0110)能级跃迁时光谱线强度的影响.     

Linearized augmented plane wave method utilizing the quadratic energy expansion of radial wave functions

Conclusions The developed version of the augmented plane wave method yields eigenvalues and eigenfunctions with higher accuracy than the standard LAPW, preserving its computational efficiency.The approximation of the exact radial solution by the Taylor expansion involving also the second energy derivative of the radial function, except for the first derivative, has two advantages. First, the energy dependence of the logarithmic derivatives atr=R is better described and, therefore, the method is less sensitive to the choice of the centre of expansionE ₀ or, equivalently, acceptably accurate eigenvalues are obtained for the broader energy region aroundE ₀. The other and probably more important advantage is that the approximate radial solutions are remarkably closer to the exact radial functions inside the muffin-tin sphere. This can be of use when evaluating the measurable quantities depending on the wave functions.     

Instanton induced green functions in the superfield formalism

We discuss in detail the supersymmetric instanton calculus of NSVZ and extend it to chiral matter fields in the, adjoint representation. The constant Green functions induced by the instanton of supersymmetricSU (2) gauge theories are calculated systematically for the cases with and without scalar vev's bigger than the scale of the gauge theory and for nonvanishing small masses of chiral fields. Oneinstanton contributions to the Green functions containing four fields without large vevs would disturb clustering; but they are argued to vanish; two-instanton effects then lead to a pattern which quantitatively agrees with factorization and the anomaly relation.     

Quantum geometrodynamics: The path integral and the initial value problem for the wave function of the universe

The wave function of the universe is obtained in the form of the functional integral over lorentzian four-geometries from the path-integral quantization of the true dynamical degrees of freedom. The algorithms for quantum averages and probability amplitudes in the Wheeler-DeWitt quantum geometrodynamics are derived and the initial value problem for the wave function in superspace of three-metrics is formulated.