相关论文: Energy Level Sets for the Morse Potential
This study combines the quantum Rubik's Cube matrix with the Benalcazar Bernevig Hughes model, defines a matrix algorithm based on the reverse process of convolution, and constructs an expression for the quantum Rubik's Cube matrix and…
In this technical note a general procedure is described to construct internally consistent splitting methods for the numerical solution of differential equations, starting from matching pairs of explicit and diagonally implicit Runge-Kutta…
For electromagnetic transient (EMT) simulation of a power system, a state-space-based approach needs to solve state-space EMT equations by using numerical integration methods, e.g., the Euler method, Runge-Kutta methods, and…
A type of adaptive finite element method for the eigenvalue problems is proposed based on the multilevel correction scheme. In this method, adaptive finite element method to solve eigenvalue problems involves solving associated boundary…
This article illustrates a completely algebraic method to obtain the energy levels of a massive spin-1 particle moving in a constant magnetic field. In the process to obtain the energy levels the wave function was written by harmonic…
A general method to describe a second-order phase transition is discussed. It starts from the energy level statistics and uses of finite-size scaling. It is applied to the metal-insulator transition (MIT) in the Anderson model of…
We investigate the charging energy level statistics of disordered interacting electrons in quantum dots by numerical calculations using the Hartree approximation. The aim is to obtain a global picture of the statistics as a function of…
In simulating physical systems, conservation of the total energy is often essential, especially when energy conversion between different forms of energy occurs frequently. Recently, a new fourth order energy-preserving integrator named MB4…
A general quantization rule for bound states of the Schrodinger equation is presented. Like fundamental theory of integral, our idea is mainly based on dividing the potential into many pieces, solving the Schr\"odinger equation, and…
We address the nonlinear properties of the double-Morse potential as a resource for single-mode quantum states due to its double-well structure and anharmonicity. We obtain analytical expressions for the ground-state wavefunction and the…
The capacitive couplings between gate-defined quantum dots and their gates vary considerably as a function of applied gate voltages. The conversion between gate voltages and the relevant energy scales is usually performed in a regime of…
In this work, we investigate the quantum dynamics of a particle subject to the Morse potential within the framework of Dunkl quantum mechanics. By employing the Dunkl derivative operator, which introduces reflection symmetry, we construct a…
An infinite sequence of potential well functions is considered. A numerical method is used for the Schr$\ddot{\text{o}}$dinger equation to obtain the energy eigenvalue spectra for a number of these potential well functions. The results for…
The supersymmetric solutions of PT-/non-PT-symmetric and non-Hermitian deformed Morse and P\"{o}schl-Teller potentials are obtained by solving the Schr\"{o}dinger equation. The Hamiltonian hierarchy method is used to get the real energy…
This paper presents the exact ground state solution for a diatomic particle system with position-dependent complex mass under action of a complex Morse potential in the quantum domain. By solving the position-dependent Schr\"odinger…
This paper presents a nonperturbative method for solving eigenproblems. This method applies to almost all potentials and provides nonperturbative approximations for any energy level. The method converts an eigenproblem into a perturbation…
We study the level statistics (second half moment $I_0$ and rigidity $\Delta_3$) and the eigenfunctions of pseudointegrable systems with rough boundaries of different genus numbers $g$. We find that the levels form energy intervals with a…
We have recently proposed a quantum control method based on the knowledge of the energy spectrum as a function of an external control parameter [Phys. Rev. Lett. {\bf 99}, 036806 (2007)]. So far, our method has been applied to connect the…
In this paper, we present continuous-stage partitioned Runge-Kutta (csPRK) methods for energy-preserving integration of Hamiltonian systems. A sufficient condition for the energy preservation of the csPRK methods is derived. It is shown…
For diatomic molecules and chains bound anharmonically by interactions such a the Lennard Jones and Morse potentials, we obtain analytical expressions for thermodynamic observables including the mean bond length, thermally averaged internal…