相关论文: Energy Level Sets for the Morse Potential

This paper investigates an efficient exponential integrator generalized multiscale finite element method for solving a class of time-evolving partial differential equations in bounded domains. The proposed method first performs the spatial…

A theory of vibrational energy relaxation based on a semiclassical treatment of the quantum master equation is presented. Using new results on the semiclassical expansion of dipole matrix elements, we show that in the classical limit the…

The electronic conductance of a molecule making contact to electrodes is determined by the coupling of discrete molecular states to the continuum electrode density of states. Interactions between bound states and continua can be modeled…

Certain superposition states of the 1-D infinite square well have transient zeros at locations other than the nodes of the eigenstates that comprise them. It is shown that if an infinite potential barrier is suddenly raised at some or all…

Many HPC applications that solve differential equations rely on the Runge-Kutta family of methods for time integration. Among these methods, the fourth-order accurate RK4 scheme is especially popular. This time integration scheme requires…

The present manuscript gives a theoretical description of the first-order phase transition in a cell fluid model with a modified Morse potential and additional repulsive interaction. In the framework of the grand canonical ensemble, the…

Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state energy in a systematic fashion, scales…

We present explicit methods for simulating diffusions whose generator is self-adjoint with respect to a known (but possibly not normalizable) density. These methods exploit this property and combine an optimized Runge-Kutta algorithm with a…

In this paper, we give a numerical analysis for the transmission eigenvalue problem by the finite element method. A type of multilevel correction method is proposed to solve the transmission eigenvalue problem. The multilevel correction…

This paper calculates the quantized energy levels of the hydrogen atom, using a metaplectic-c prequantization bundle and a definition of a quantized energy level that was introduced by the author in a previous paper. The calculation makes…

The influence of isolated impurity atoms on the electron energy spectrum in a parabolic quantum dot in quantizing magnetic field is studied. The impurity potential is approximated by a Gaussian separable operator which allows one to obtain…

In this paper, we discuss the compatibility between the rotating-wave and the adiabatic approximations for controlled quantum systems. Although the paper focuses on applications to two-level quantum systems, the main results apply in higher…

The self-energy-functional approach proposed recently is applied to the single-band Hubbard model at half-filling to study the Mott-Hubbard metal-insulator transition within the most simple but non-trivial approximation. This leads to a…

In this survey, we provide an in-depth investigation of exponential Runge-Kutta methods for the numerical integration of initial-value problems. These methods offer a valuable synthesis between classical Runge-Kutta methods, introduced more…

In this study, we obtain the approximate analytical solutions of the radial Schrodinger equation for the New Generalized Morse-Like Potential in arbitrary dimensions by using the Nikiforov Uvarov Method. Energy eigenvalues and corresponding…

By introducing the shape invariant Lie algebra spanned by the SUSY ladder operators plus the unity operator, a new basis is presented for the quantum treatment of the one-dimensional Morse potential. In this discrete, complete orthonormal…

Elegant and mathematically rigorous methods of the quantum inverse theory are difficult to put into practice because there is always some lack of needful input information. In this situation, one may try to construct a reference potential,…

The bootstrap is a technique recently developed to get energy eigenvalues of bound states and correlation functions. There are three crucial steps - recursive equations, positivity constraints, search space. We calculate recursive equations…

We present the renormalized perturbation series for the energy spectrum of the parabolic quantum dot with 2 -- 5 electrons considering ground and the lowest excited states. The proper classification of asymptotic energy levels is performed…

The computation of interaction energies on noisy intermediate-scale quantum (NISQ) computers appears to be challenging with straightforward application of existing quantum algorithms. For example, use of the standard supermolecular method…