Energy eigenvalues from an analytical transfer matrix method

A detailed procedure based on an analytical transfer matrix method is presented to solve bound-state problems. The derivation is strict and complete. The energy eigenvalues for an arbitrary one-dimensional potential can be obtained by the method. The anharmonic oscillator potential and the rational potential are two important examples. Checked by numerical techniques, the results for the two potentials by the present method are proven to be exact and reliable.

Energy Spectrum for a Short-Range 1/r Singular Potential with a Non-Orbital Barrier Using the Asymptotic Iteration Method

Using the asymptotic iteration method, we obtain the S-wave solution for a short-range three-parameter central potential with 1/r singularity and with a non-orbital barrier. To the best of our knowledge, this is the first attempt at calculating the energy spectrum for this potential, which was introduced by H. Bahlouli and A. D. Alhaidari and for which they obtained the “potential parameter spectrum”. Our results are also independently verified using a direct method of diagonalizing the Hamiltonian matrix in the J-matrix basis.

Dry-type AMDT Fault Detection Based on Vibration Signal Analysis by Wavelet Packet

Amorphous metal distribution transformers(AMDT)are widely used in power grids due to their low no-load loss.Many scholars have carried out research on the fault detection of transformer windings,tap changers and the other parts.However,due to the high magnetostriction of the amorphous alloy,the vibration generated by AMDT during operation will cause various mechanical failures.This paper studies the vibration characteristics of SCBH 15-200/100 AMDT through no-load tests to find some mechanical failures of AMDT.The installation position of the vibration sensor in AMDT are determined according to finite element analysis(FEA)of the magnetic flux density distribution and modal analysis,and the vibration analyses are performed under different operating conditions of AMDT.The wavelet packet transform(WPT)is used to perform detailed analysis of the vibration signal in the time domain and frequency domain to obtain the energy characteristic value of each frequency band,and it includes the frequency spectrum and waveform data under normal and fault conditions.After obtaining the energy characteristic thresholds of different frequency bands under different conditions,the operating status can be detected by comparing test data with the thresholds.The operation condition including mechanical failures induced by magnetostrictive actions can be accurately determined by the energy characteristic value,such as loose nuts and stress,etc.

Bound State Solutions of Schrodinger Equation for Generalized Morse Potential with Position-Dependent Mass

The effective mass one-dimensional Schroedinger equation for the generalized Morse potential is solved by using Nikiforov-Uvarov method. Energy eigenvalues and corresponding eigenfunctions are computed analytically. The results are also reduced to the constant mass case. Energy eigenvalues are computed numerically for some diatomic molecules. They are in agreement with the ones obtained before.

Quantization rules for low dimensional quantum dots

This paper applies the analytical transfer matrix method （ATMM） to calculate energy eigenvalues of a particle in low dimensional sharp confining potential for the first time, and deduces the quantization rules of this system. It presents three cases in which the applied method works very well. In the first quantum dot, the energy eigenvalues and eigenfunction are obtained, and compared with those acquired from the exact numerical analysis and the WKB （Wentzel, Kramers and Brillouin） method; in the second or the third case, we get the energy eigenvalues by the ATMM, and compare them with the EBK （Einstein, Brillouin and Keller） results or the wavefunction outcomes. From the comparisons, we find that the semiclassical method （WKB, EBK or wavefunction） is inexact in such systems.

Six—Parameter Exponential—Type Potential and the Identity for the Exponential—Type Potentials

We propose a six-parameter exponential-type potential (SPEP), which has been shown to be a shape-invariant potential with a translation of parameters. For this reducible potential, the exact energy levels are obtained byusing the supersymmetric shape invariance technique. Choosing appropriate parameters, four classes of exponential-typepotentials and their exact energy spectra are reduced from the SPEP and a general energy level formula, respectively.Each class shows the identity except for the different definitions of parameters.

Analysis of Energy Eigenvalue in Complex Ginzburg–Landau Equation

In this paper, we consider the two-dimensional complex Ginzburg–Landau equation(CGLE) as the spatiotemporal model, and an expression of energy eigenvalue is derived by using the phase-amplitude representation and the basic ideas from quantum mechanics. By numerical simulation, we find the energy eigenvalue in the CGLE system can be divided into two parts, corresponding to spiral wave and bulk oscillation. The energy eigenvalue of spiral wave is positive, which shows that it propagates outwardly; while the energy eigenvalue of spiral wave is negative, which shows that it propagates inwardly. There is a necessary condition for generating a spiral wave that the energy eigenvalue of spiral wave is greater than bulk oscillation. A wave with larger energy eigenvalue dominates when it competes with another wave with smaller energy eigenvalue in the space of the CGLE system. At the end of this study, a tentative discussion of the relationship between wave propagation and energy transmission is given.

Duffin-Kemmer-Petiau equation under Hartmann ring-shaped potential

We solve the DufRn-Kemmer-Petiau（DKP） equation in the presence of Hartmann ring-shaped potential in（3＋l）-dimensional space-time.We obtain the energy eigenvalues and eigenfunctions by the Nikiforov-Uvarov（NU）method.