A New Class of Exactly Solvable Models within the Schrodinger Equation with Position Dependent Mass

The study of physical systems endowed with a position-dependent mass (PDM) remains a fundamental issue of quantum mechanics. In this paper we use a new approach, recently developed by us for building the quantum kinetic energy operator (KEO) within the Schrodinger equation, in order to construct a new class of exactly solvable models with a position varying mass, presenting a harmonic-oscillator-like spectrum. To do so we utilize the formalism of supersymmetric quantum mechanics (SUSY QM) along with the shape invariance condition. Recent outcomes of non-Hermitian quantum mechanics are also taken into account.

THE DISLOC ATION EQU ATIONS OF A SIMPLE CUBIC CRYSTAL IN THE ISOTROPIC APPROXIMATION-A SOLVABLE MODEL

The dislocation equations of a simple cubic lattice have been obtained by using Green＇s function method based on the discrete lattice theory with the coefficients of the secondorder differential terms and the integral terms have been given explicitly in advance. The simple cubic lattice we have discussed is a solvable model, which is obtained according to the lattice statics and the symmetry principle and can verify and validate the dislocation lattice theory. It can present unified dislocation equations which are suitable for most of metals with arbitral lattice structures. Through comparing the results of the present solvable model with the dislocation lattice theory, it can be seen that, the coefficients of integral terms of the edge and screw components we obtain are in accordance with the results of the dislocation lattice theory, however, the coefficient of the second-order differential term of the screw component is not in agreement with the result of the dislocation lattice theory. This is mainly caused by the reduced dynamical matrix of the surface term, which is the essence to obtain the dislocation equation. According to the simple cubic solvable model, not only the straight dislocations but also the curved dislocations, such as the kink, can be investigated further.

A SOLVABLE ONE-DIMENSIONAL ALLOCATION DECISION MODEL OF RENEWABLE RESOURCES

In the paper, the determinate atlecation decision model and the probabilistic allocation decision model of a kind of renewable resource are separatly studied by means of dynamic programming, and the optimal allocation policy is given under some special conditions.

Effects of electron correlation on superconductivity in the Hatsugai-Kohmoto model

Understanding how electrons form pairs in the presence of strong electron correlations demands going beyond the BCS paradigm.We study a correlated superconducting model where the correlation effects are accounted for by a U term local in momentum space.The electron correlation is treated exactly while the electron pairing is treated approximately using the mean-field theory.The self-consistent equation for the pair potential is derived and solved.Somewhat contrary to expectation,a weak attractive U comparable to the pair potential can destroy the superconductivity,whereas for weak to intermediate repulsive U,the pair potential can be enhanced.The fidelity of the mean-field ground state is calculated to describe the strength of the elelectron correlation.We show that the pair potential is not equal to the single-electron superconducting gap for the strongly correlated superconductors,in contrast to the uncorrelated BCS limit.

Dirac operator on the sphere with attached wires

An explicitly solvable model for tunnelling of relativistic spinless particles through a sphere is suggested. The model operator is constructed by an operator extensions theory method from the orthogonal sum of the Dirac operators on a semi- axis and on the sphere. The transmission coefficient is obtained. The dependence of the transmission coefficient on the particle energy has a resonant character. One observes pairs of the Breit-Wigner and the Fano resonances. It correlates with the corresponding results for a non-relativistic particle.

Exact solution of U(5)–O(6) transitional description in interacting boson model with two-particle and two-hole configuration mixing

The exact solution of the U(5)-O(6)transitional description in the interacting boson model with twoparticle and two-hole configuration mixing is derived based on the Bethe ansatz approach.The Bethe ansatz equations are provided to determine the model’s eigenstates and corresponding eigen-energies.N=2 and N=4 cases are considered as examples to demonstrate the solution features.As an example of the application,some low-lying level energies and B(E2)ratios of 108Cd are fitted and compared with the corresponding experimental data.