Convergent Iterative Solutions of Schroedinger Equation for a Generalized Double Well Potential

We present an explicit convergent iterative solution for the lowest energy state of the Schroedinger equation with a generalized double well potential $V=\frac{g^2}{2}(x^2-1)^2(x^2+a)$. The condition for the convergence of the iteration procedure and the dependence of the shape of the groundstate wave function on the parameter $a$ are discussed.Comment: 23 pages, 7 figure

A Convergent Iterative Solution of the Quantum Double-well Potential

We present a new convergent iterative solution for the two lowest quantum wave functions $\psi_{ev}$ and $\psi_{od}$ of the Hamiltonian with a quartic double well potential $V$ in one dimension. By starting from a trial function, which is by itself the exact lowest even or odd eigenstate of a different Hamiltonian with a modified potential $V+\delta V$, we construct the Green's function for the modified potential. The true wave functions, $\psi_{ev}$ or $\psi_{od}$, then satisfies a linear inhomogeneous integral equation, in which the inhomogeneous term is the trial function, and the kernel is the product of the Green's function times the sum of $\delta V$, the potential difference, and the corresponding energy shift. By iterating this equation we obtain successive approximations to the true wave function; furthermore, the approximate energy shift is also adjusted at each iteration so that the approximate wave function is well behaved everywhere. We are able to prove that this iterative procedure converges for both the energy and the wave function at all $x$.Comment: 76 pages, Latex, no figure, 1 tabl

A New Method to Derive Low-Lying N-dimensional Quantum Wave Functions by Quadratures Along a Single Trajectory

We present a new method to derive low-lying N-dimensional quantum wave functions by quadrature along a single trajectory. The N-dimensional Schroedinger equation is cast into a series of readily integrable first order ordinary differential equations. Our approach resembles the familiar W.K.B. approximation in one dimension, but is designed to explore the classically forbidden region and has a much wider applicability than W.K.B.. The method also provides a perturbation series expansion and the Green's functions of the wave equation in N-dimension, all by quadratures along a single trajectory. A number of examples are given for illustration, including a simple algorithm to evaluate the Stark effect in closed form to any finite order of the electric field.Comment: 69 pages, Latex, no figure, no table; more ackowledgment added, typos correcte

A High-gain and Low-scattering Waveguide Slot Antenna of Artificial Magnetic Conductor Octagonal Ring Arrangement

A novel design of high-gain and low-scattering waveguide slot antenna is proposed in this paper. Firstly the scattering pattern of artificial magnetic conductor (AMC) composite surface is estimated by array factor analysis method. The comparison between octagonal ring arrangement and chessboard arrangement proves that the former arrangement has the characteristic of diffuseness-like and expands the bandwidth of radar cross section (RCS) reduction. Secondly, the metal surface of waveguide slot antenna (WSA) is replaced by the octagonal ring arrangement composite surface (ORACS). The gain is improved because of spurious radiation units which are around the slot. At the same time using the phase cancellation principle, a backscatter null achieves RCS reduction in the vertical direction. Experimental results show that the novel antenna after loading with the ORACS, the gain is improved by 5dB; the bandwidth of RCS reduction (reduction greater than 10dB) is 5.24-5.92 GHz

Performance investigation of hybrid excited switched flux permanent magnet machines using frozen permeability method

This study investigates the electromagnetic performance of a hybrid excited switched flux permanent magnet (SFPM) machine using the frozen permeability (FP) method. The flux components due to PMs, field excitation windings and armature windings have been separated using the FP method. It has been used to separate the torque components due to the PMs and excitations, providing a powerful insight into the torque generation mechanism of hybrid excited SFPM machines. It also allows the accurate calculation of d- and q-axis inductances, which will then be used to calculate the torque, power and power factor against rotor speed to compare the relative merits of hybrid excited SFPM machines with different types of PMs (i.e. NdFeB, SmCo and Ferrite). This offers the possibility of choosing appropriate PMs for different applications (maximum torque or maximum speed). Although only one type of hybrid excited PM machine has been employed to carry out the investigations, the method used in this study can also be extended to other hybrid excited PM machines. The predicted results have been validated by tests

Effects of Nano-Sized Al on the Combustion Performance of Fuel Rich Solid Rocket Propellants

Several industrial- and research – type fuel rich solid rocket propellants containing nano-metric aluminum metal particles, featuring the same nominal composition, were prepared and experimentally analyzed. The effects of nano-sized aluminum (nAl) on the rheological properties of metal/HTPB slurries and fuel rich solid propellant slurries were investigated. The energetic properties (heat of combustion and density) and the hazardous properties (impact sensitivity and friction sensitivity) of propellants prepared were analyzed and the properties mentioned above compared to those of a conventional aluminized (micro-Al, mAl) propellant. The strand burning rate and the associated combustion fl ame structure of propellants were also determined. The results show that nAl powder is nearly "round" or "ellipse" shaped, which is different from the tested micrometric Al used as a reference metal fuel. Two kinds of Al (nAl and mAl) powder can be dispersed in HTPB binder suffi ciently. The density of propellant decreases with increasing mass fraction of nAl powder; the measured heat of combustion, friction sensitivity, and impact sensitivity of propellants increase with increasing mass fraction of nAl powder in the formulation. The burning rates of fuel rich propellant increase with increasing pressure, and the burning rate of the propellant loaded with 20% mass fraction of nAl powder increases 77.2% at 1 MPa, the pressure exponent of propellant increase a little with increasing mass fraction of nAl powder in the explored pressure ranges

Protons in near earth orbit

The proton spectrum in the kinetic energy range 0.1 to 200 GeV was measured by the Alpha Magnetic Spectrometer (AMS) during space shuttle flight STS-91 at an altitude of 380 km. Above the geomagnetic cutoff the observed spectrum is parameterized by a power law. Below the geomagnetic cutoff a substantial second spectrum was observed concentrated at equatorial latitudes with a flux ~ 70 m^-2 sec^-1 sr^-1. Most of these second spectrum protons follow a complicated trajectory and originate from a restricted geographic region.Comment: 19 pages, Latex, 7 .eps figure

Search for antihelium in cosmic rays

The Alpha Magnetic Spectrometer (AMS) was flown on the space shuttle Discovery during flight STS-91 in a 51.7 degree orbit at altitudes between 320 and 390 km. A total of 2.86 * 10^6 helium nuclei were observed in the rigidity range 1 to 140 GV. No antihelium nuclei were detected at any rigidity. An upper limit on the flux ratio of antihelium to helium of < 1.1 * 10^-6 is obtained.Comment: 18 pages, Latex, 9 .eps figure

A Study of Cosmic Ray Secondaries Induced by the Mir Space Station Using AMS-01

The Alpha Magnetic Spectrometer (AMS-02) is a high energy particle physics experiment that will study cosmic rays in the $\sim 100 \mathrm{MeV}$ to $1 \mathrm{TeV}$ range and will be installed on the International Space Station (ISS) for at least 3 years. A first version of AMS-02, AMS-01, flew aboard the space shuttle \emph{Discovery} from June 2 to June 12, 1998, and collected $10^8$ cosmic ray triggers. Part of the \emph{Mir} space station was within the AMS-01 field of view during the four day \emph{Mir} docking phase of this flight. We have reconstructed an image of this part of the \emph{Mir} space station using secondary $\pi^-$ and $\mu^-$ emissions from primary cosmic rays interacting with \emph{Mir}. This is the first time this reconstruction was performed in AMS-01, and it is important for understanding potential backgrounds during the 3 year AMS-02 mission.Comment: To be submitted to NIM B Added material requested by referee. Minor stylistic and grammer change