The spin symmetry for deformed generalized Pöschl-Teller potential

In the case of spin symmetry we solve the Dirac equation with scalar and vector deformed generalized Pöschl-Teller (DGPT) potential and obtain exact energy equation and spinor wave functions for s-wave bound states. We find that there are only positive energy states for bound states in the case of spin symmetry based on the strong regularity restriction condition λ<−η for the wave functions. The energy eigenvalue approaches a constant when the potential parameter α goes to zero. Two special cases such as generalized PT potential and standard PT potential are also briefly discussed.     

A singular position-dependent mass particle in an infinite potential well

An unusual singular position-dependent-mass particle in an infinite potential well is considered. The corresponding Hamiltonian is mapped through a point-canonical-transformation and an explicit correspondence between the target Hamiltonian and a Pöschl-Teller type reference Hamiltonian is obtained. New ordering ambiguity parametric setting are suggested.     

Generalized Morse and Pöschl-Teller potentials: The connection via Schrödinger equation

A systematic and unified treatment to connect the Schrödinger equation for generalized Morse and Pöschl-Teller potentials, generated by supersymmetry quantum mechanics, is used. An algebraic treatment of bound-state problems is presented.     

Hidden supersymmetry in quantum bosonic systems

We show that some simple well-studied quantum mechanical systems without fermion (spin) degrees of freedom display, surprisingly, a hidden supersymmetry. The list includes the bound state Aharonov-Bohm, the Dirac delta and the Pöschl-Teller potential problems, in which the unbroken and broken N = 2 supersymmetry of linear and nonlinear (polynomial) forms is revealed.     

Classical motion and coherent states for Pöschl-Teller potentials

The trigonometric and hyperbolic Pöschl-Teller potentials are dealt with from the point of view of classical and quantum mechanics. We show that there is a natural correspondence between the algebraic structure of these two approaches for both kind of potentials. Then, the coherent states are constructed and the appropriate classical variables are compared with the expected values of their corresponding quantum operators.     

Solutions of Dirac equations with the Pöschl-Teller potential

By using the basic concepts of the supersymmetric quantum mechanics formalism and the function analysis method, we solve the Dirac equation with vector and scalar potentials and obtain the bound-state solutions for the nuclei in the relativistic P?schl-Teller potential. All of the analyses are prepared under the conditions of the exact spin symmetry and pseudospin symmetry. The exact energy equation and corresponding two-component spinor wave functions for s -wave bound states are obtained analytically.     

Effective-Mass Schrödinger Equation and Generation of Solvable Potentials

A one-dimensional Schrödinger equation with position-dependent effective mass in the kinetic-energy operator is studied in the framework of an so(2,1) algebra. New mass-deformed versions of Scarf II, Morse, and generalized Pöschl-Teller potentials are obtained. Consistency with the intertwining condition is pointed out.     

Energy spectra of the hyperbolic and second Pöschl-Teller like potentials solved by new exact quantization rule

A new exact quantization rule simplifies the calculation of the energy levels for the exactly solvable quantum system. In this work we calculate the energy levels of the Schrödinger equation with the hyperbolic potential by this quantization rule. The corresponding eigenfunction is also derived for completeness. The second Pöschl-Teller like potential case is also carried out.     

Josephson Dynamics of a Bose-Einstein Condensate Trapped in a Double-Well Potential

The Josephson equations for a Bose Einstein Condensate gas trapped in a double-well potential are derived with the two-mode approximation by the Gross Pitaevskii equation. The dynamical characteristics of the equations are obtained by the numerical phase diagrams. The nonlinear self-trapping effect appeared in the phase diagrams are emphatically discussed, and the condition EcN 〉 4E3 is presented.     

凝聚炸药中超压爆轰的实验研究

 采用飞片碰撞技术，在TNT/RDX（40/60）炸药中获得了2.5倍于正常爆轰的最大超压值，得到了超压爆轰下爆轰产物物态方程p=Aρ^{k+A₁(p-p_J)}（p－爆压，单位GPa，ρ－密度，单位kg/m³，A=ρ_J/ρ^k_J，p_J=27.06 GPa，ρ_J=2.3×10³ kg/m³，k=2.77，A₁=2.7×10^-3 GPa^-1，下表J代表正常爆轰状态）。该方程还可以较好地描述超压爆轰产物的二次冲击状态。     

Electronic Curves Crossing in Methyl Iodide by Spin--Orbit Ab Initio Calculation

An ab initio investigation of electronic curve crossing in a methyl iodide molecule is carried out using spin-orbit multiconfigurational quasidegenerate perturbation theory. The one-dimensional rigid potential curves and optimized effective curves of low-lying states, including spin-orbit coupling and relativistic effects, are calculated. The spin-orbit electronic curve crossing between ^3Qo＋ and ^1Q1, and the shadow minimum in potential energy curve of ^3Qo＋ at large internuclear distance are found in both sets of the curves according to the present calcu- lations. The crossing position is in the range of Re-1 = 0.2370 3：0.0001 nm. Comparisons with other reports are presented.     

PT-Symmetric Calogero-Type Model

We examine angular (Pöschl-Teller) Schrödinger equation. The domain is deformed into the complex plane. We derive its solutions that are subject to Dirichlet boundary conditions.     

Raman and X-Ray Investigation of Pyrope Garnet （Mg0.76Fe0.14Ca0.10）3Al2Si3O12 under High Pressure

The compressional behavlour of natural pyrope garnet is investigated by using angle-dlspersive synchrotron radiation x-ray diffraction and Raman spectroscopy in a diamond anvil cell at room temperature. The pressureinduced phase transition does not occur under given pressure. The equation of state of pyrope garnet is determined under pressure up to 25.3 GPa. The bulk modulus KTO is 199 GPa, with its first pressure derivative K′TO fixed to 4. The Raman spectra of pyrope garnet are studied. A new Raman peak nearly at 743 cm^-1 is observed in a bending vibration of the SiO4 tetrahedra frequency range at pressure of about 28 GPa. We suggest that the new Raman peak results from the lattice distortion of the SiO4 tetrahedra. All the Raman frequencies continuously increase with the increasing pressure. The average pressure derivative of the high frequency modes （650-1000 cm^-1） is larger than that of the low frequency （smaller than 650 cm^-1）. Based on these data, the mode Grǖneisen parameters for pyrope are obtained.     

Approximate Solutions of the Schrödinger Equation for the Eckart Potential and Its Parity-Time-Symmetric Version Including Centrifugal Term

The energy eigenvalues and eigenfunctions of the Schrödinger equation for Eckart potential as well as the parity-time-symmetric version of the potential in three dimensions with the centrifugal term are investigated approximately by using the Nikiforov-Uvarov method. To show the accuracy of our results, we calculate the energy eigenvalues for various values of n and l. It is found that the results are in good agreement with the numerical solutions for short-range potential (large a). For the case of 1/a i/a, the potential is also studied briefly.     

Simultaneous Generation of Multi-Wavelength Laser from Nd:YAG Crystals in a Cruciform Cavity

A cruciform cavity is presented for multi-wavelength laser generation. On the basis of considering the optimal power ratio and good spatial overlap of the two fundamental beams, the maximum output power of 589 nm laser reaches 3.5 W when the pumping power of Nd：YAG A and Nd：YAG B are 311.5 W and 261.8 W, respectively. At the same time, the other wavelength lasers are also obtained with the output power distribution of 2.5 W at 66Onto, 15 W at 532nm, lOOmW at 1319nm and 240mW at 1064nm. The corresponding beam quality factors are M^2 x = 4.93, M^2 y = 5.01 at 589nm, M^2z = 4.51, M^2 y = 4.85 at 660hm, and M^2 x = 4.12, M^2 y = 3.96 at 532nm, respectively. The instabilities of the three visible lights are measured, which are also less than 2% within three hours.     

Schrödinger equation with delta potential in superspace

A superspace version of the Schrödinger equation with a delta potential is studied using Fourier analysis. An explicit expression for the energy of the single bound state is found as a function of the super-dimension M in case M is smaller than or equal to 1. In the case when there is one commuting and 2n anti-commuting variables also the wave function is given explicitly.     

Pressure-induced phase transition of wulfenite

The in-situ high-pressure structures of wulfenite have been investigated by means of angular dispersive X-ray diffraction with diamond anvil cell and synchrotron radiation. In the pressure up to 22.9 GPa, a pressure-induced scheelite-to-fergusonite transition is observed at about 10.6 GPa. The pressure dependence for the lattice parameters of wulfenite is reported, and the axial compression coefficients Ka₀=－1.36×10^－3 GPa^－1 and Kc₀= －2.78×10^－3 GPa^－1 are given. The room-temperature isothermal bulk modulus is also obtained by fitting the P-V data using the Murnaghan equation of state.

     

Dissociation Energies of Diatomic Molecules

Molecular dissociation energies of 10 electronic states of alkali molecules of KH, ^7LiD, ^7 LiH, ^6LiH, NaK, NaLi and NaRb are studied using the highest three accurate vibrational energies of each electronic state, and an improved parameter-free analytical formula which is obtained starting from the LeRoy Bernstein vibrational energy expression near the dissociation limit. The results show that as long as the highest three vibrational energies are accurate, the current analytical formula will give accurate theoretical dissociation energies De^theory, which are in excellent agreement with the experimental dissociation energies De^expt.     

Path integration on Darboux spaces

In this paper, the Feynman path integral technique is applied to two-dimensional spaces of nonconstant curvature: these spaces are called Darboux spaces D _I-D _IV. We start each consideration in terms of the metric and then analyze the quantum theory in the separable coordinate systems. The path integral in each case is formulated and then solved in the majority of cases; the exceptions being the quartic oscillators where no closed solution is known. The required ingredients are the path integral solutions of the linear potential, the harmonic oscillator, the radial harmonic oscillator, the modified Pöschl-Teller potential, and the spheroidal wave functions. The basic path integral solutions, which appear here in a complicated way, have been developed in recent work and are known. The final solutions are represented in terms of the corresponding Green’s functions and the expansions into the wave functions. We also sketch some limiting cases of the Darboux spaces, where spaces of constant negative and zero curvature emerge.