Quasilinearization Method and Summation of the WKB Series

Solutions obtained by the quasilinearization method (QLM) are compared with the WKB solutions. Expansion of the $p$-th QLM iterate in powers of $\hbar$ reproduces the structure of the WKB series generating an infinite number of the WKB terms with the first $2^p$ terms reproduced exactly. The QLM quantization condition leads to exact energies for the P\"{o}schl-Teller, Hulthen, Hylleraas, Morse, Eckart potentials etc. For other, more complicated potentials the first QLM iterate, given by the closed analytic expression, is extremely accurate. The iterates converge very fast. The sixth iterate of the energy for the anharmonic oscillator and for the two-body Coulomb Dirac equation has an accuracy of 20 significant figures

Effects of Nacelle configuration/position on performance of subsonic transport

An experimental study was conducted to explore possible reductions in installed propulsion system drag due to underwing aft nacelle locations. Both circular (C) and D inlet cross section nacelles were tested. The primary objectives were: to determine the relative installed drag of the C and D nacelle installations; and, to compare the drag of each aft nacelle installation with that of a conventional underwing forward, drag of each aft nacelle installation with that of a conventional underwing forward, pylon mounted (UTW) nacelle installation. The tests were performed in the NASA-Langley Research Center 16-Foot Transonic Wind Tunnel at Mach numbers from 0.70 to 0.85, airplane angles of attack from -2.5 to 4.1 degrees, and Reynolds numbers per foot from 3.4 to 4.0 million. The nacelles were installed on the NASA USB full span transonic transport model with horizontal tail on. The D nacelle installation had the smallest drag of those tested. The UTW nacelle installation had the largest drag, at 6.8 percent larger than the D at Mach number 0.80 and lift coefficient (C sub L) 0.45. Each tested configuration still had some interference drag, however. The effect of the aft nacelles on airplane lift was to increase C sub L at a fixed angle of attack relative to the wing body. There was higher lift on the inboard wing sections because of higher pressures on the wing lower surface. The effects of the UTW installation on lift were opposite to those of the aft nacelles

Spin dependent operators in correlated gaussian bases

In their textbook, Suzuki and Varga [Y. Suzuki and K. Varga, {\em Stochastic Variational Approach to Quantum-Mechanical Few-Body Problems} (Springer, Berlin, 1998)] present the stochastic variational method with the correlated Gaussian basis in a very exhaustive way. The matrix elements for central potentials are put under a pleasant form but the elements for spin dependent operators, when treated, are given as very cumbersome expressions. In this paper, we find a lot of new formulae for those elements. Their expressions are given in terms of the same geometrical functions that appear in the case of central potentials. These functions get therefore a universal status; this property is very useful for numerical applications.Comment: 16 page

Independent Eigenstates of Angular Momentum in a Quantum N-body System

The global rotational degrees of freedom in the Schr\"{o}dinger equation for an $N$-body system are completely separated from the internal ones. After removing the motion of center of mass, we find a complete set of $(2\ell+1)$ independent base functions with the angular momentum $\ell$. These are homogeneous polynomials in the components of the coordinate vectors and the solutions of the Laplace equation, where the Euler angles do not appear explicitly. Any function with given angular momentum and given parity in the system can be expanded with respect to the base functions, where the coefficients are the functions of the internal variables. With the right choice of the base functions and the internal variables, we explicitly establish the equations for those functions. Only (3N-6) internal variables are involved both in the functions and in the equations. The permutation symmetry of the wave functions for identical particles is discussed.Comment: 24 pages, no figure, one Table, RevTex, Will be published in Phys. Rev. A 64, 0421xx (Oct. 2001

Photoionization accompanied by excitation at intermediate photon energies

We calculate the photoionization with excitation-to photoionization ratios for atomic helium and heliumlike ions at intermediate values of the photon energies. The final state interactions between the electrons are included in the lowest order of their Sommerfeld parameter. This enables us, in contrast to purely numerical calculations to investigate the roles of various mechanisms contributing beyond the high energy limit. The system of the two bound electrons is described by the functions obtained by the Correlation Function Hyperspherical Harmonic Method. For the case of heliumlike ions we present the high energy limits as power expansion in inverse charge of the nucleus. We analyse the role of excitation of states with the nonzero orbital momenta.Comment: 3 figure