相关论文: Energy Level Sets for the Morse Potential
Two-dimensional PT-symmetric quantum-mechanical systems with the complex cubic potential V_{12}=x^2+y^2+igxy^2 and the complex Henon-Heiles potential V_{HH}=x^2+y^2+ig(xy^2-x^3/3) are investigated. Using numerical and perturbative methods,…
The recently-introduced relaxation approach for Runge-Kutta methods can be used to enforce conservation of energy in the integration of Hamiltonian systems. We study the behavior of implicit and explicit relaxation Runge-Kutta methods in…
Supersymmetric solution of PT-/non-PT-symmetric and non-Hermitian Morse potential is studied to get real and complex-valued energy eigenvalues and corresponding wave functions. Hamiltonian Hierarchy method is used in the calculations
Experimental results from literature show equidistant energy levels in thin Bi films on surfaces, suggesting a harmonic oscillator description. Yet this conclusion is by no means imperative, especially considering that any measurement only…
Exactly solvable rererence potentials of several smoothly joined Morse-type components were constructed for the lowest two excimer states of Ar2 molecule. The parameters of the potentials have been ascertained by fitting to the experimental…
We use a power-series expansion to calculate the eigenvalues of anharmonic oscillators bounded by two infinite walls. We show that for large finite values of the separation of the walls, the calculated eigenvalues are of the same high…
We discuss the coherent states for PT-/non-PT-Symmetric and non-Hermitian generalized Morse Potential obtained by using path integral formalism over the holomorphic coordinates. We transform the action of generalized Morse potential into…
Motivated by the benefits of multi-energy integration, this paper establishes a bi-level two-stage framework based on transactive control, in order to achieve optimal energy provision among interconnected multi-energy systems (MESs). At the…
The grand potential of a system of interacting electrons is considered as a stationary point of a self-energy functional. It is shown that a rigorous evaluation of the functional is possible for self-energies that are representable within a…
Applied to the master equation, the usual numerical integration methods, such as Runge-Kutta, become inefficient when the rates associated with various transitions differ by several orders of magnitude. We introduce an integration scheme…
The ACME collaboration has recently reported a new bound on the electric dipole moment (EDM) of the electron, $|d_e|< 1.1 \times 10^{-29}\, {\rm e\cdot cm}$ at 90$\%$ confidence level, reaching an unprecedented accuracy level. This can…
This paper proposes a very simple perturbative technique to calculate the low-lying eigenvalues and eigenstates of a parity-symmetric quantum-mechanical potential. The technique is to solve the time-independent Schroedinger eigenvalue…
Potential wells are employed to constrain quantum particles into forming discrete energy levels, acting as artificial few-level systems. In contrast, an anti-parity-time ($\mathcal{PT}$) symmetric system can have a single pair of real…
Path integral solutions are obtained for the the PT-/non-PT-Symmetric and non-Hermitian Morse Potential. Energy eigenvalues and the corresponding wave functions are obtained.
We consider the effect of a local perturbation on the energy levels of a system described by random matrix theory. An analytic expression for the joint distribution function of initial and final energy levels is obtained. In the case of…
Motivated by various benefits of multi-energy integration, this paper establishes a bi-level framework based on transactive control to realize energy optimization among multiple interconnected energy hubs (EHs). A storage-energy-equivalent…
We consider the form of the current-voltage curves generated when tunneling spectroscopy is used to measure the energies of individual electronic energy levels in nanometer-scale systems. We point out that the voltage positions of the…
An exact quantization rule for the Schr\"{o}dinger equation is presented. In the exact quantization rule, in addition to $N\pi$, there is an integral term, called the quantum correction. For the exactly solvable systems we find that the…
The conditioning of implicit Runge-Kutta (RK) integration for linear finite element approximation of diffusion equations on general anisotropic meshes is investigated. Bounds are established for the condition number of the resulting linear…
Manipulating energy levels while controlling the electron localization is an essential step for many applications of confined systems. In this paper we demonstrate how to achieve electron localization and induce energy level oscillation in…