Related papers: Schr\"odinger equation solved for the hydrogen mol…
The approximate bound state solutions of the Schrodinger equation with shifted Deng-Fan potential was obtained via proper quantization rule. The energy spectra for the homogenous diatomic molecules (H2, I2); the heterogeneous diatomic…
The Rydberg formula along with the Ritz quantum defect ansatz has been a standard theoretical tool used in atomic physics since before the advent of quantum mechanics, yet this approach has remained limited by its non-relativistic…
Despite the fact that the calculations of drag coefficient and pressure distribution for airfoils can be completed by using Navier-Stoke's equation with help of experimental parameters and advanced computer programming, a simple theoretical…
We transform the Schr\"odinger wave equation to a nine-parameter Heun-type differential equation. Using our solutions of the latter in [J. Math. Phys. 59 (2018) 113507], we are able to identify the associated potential function, energy…
An accurate assessment of the hyperon-nucleon interaction is of great interest in view of recent observations of very massive neutron stars. The challenge is to build a realistic interaction that can be used over a wide range of masses and…
Students in a quantum mechanics course are often introduced to the Schr\"odinger equation as the standard mathematical tool. However, rarely do students develop an understanding as to why the equation is the choice for modeling quantum…
A new approach to find exact solutions to one--dimensional quantum mechanical systems is devised. The scheme is based on the introduction of a potential function for the wavefunction, and the equation it satisfies. We recover known…
Schrodinger path to the quantum mechanical wave equation was heuristic and guided more by physical intuition than formal deduction. Here we derive the Schrodinger equation for the particle wave function, assuming that it has a meaning of…
We relax the usual diagonal constraint on the matrix representation of the eigenvalue wave equation by allowing it to be tridiagonal. This results in a larger solution space that incorporates an exact analytic solution for the non-central…
The proton, deuteron and triton masses can be determined relative to the electron mass via rovibrational spectroscopy of molecular hydrogen ions. This has to occur via comparison of the experimentally measured transition frequencies and the…
The Hartree-Fock-Rothaan equations are solved for He-like ions using the iterative self-consistent method. New complete and orthonormal sets of exponential-type orbitals are employed as the basis. These orbitals satisfy the orthonormality…
The problem of soliton-soliton force is revisited. From the exact two solitons solution of a nonautonomous Gross-Pitaevskii equation, we derive a generalized formula for the mutual force between two solitons. The force is given for…
Bound states of hyperbolic potential is investigated by means of a generalized pseudospectral method. Significantly improved eigenvalues, eigenfunctions are obtained efficiently for arbitrary $n, \ell$ quantum states by solving the relevant…
In this paper, we use the latest results of the ultra-high accuracy 1S-2S transition experiments in hydrogen atom to constrain the forms of the deformed dispersion relation in the nonrelativistic limit. For the leading correction of the…
The closed form of the first order non-linear differential equation that is satisfied by the effective range within the variable phase formulation of scattering theory is discussed. It is shown that the conventional method of determining…
Highly accurate measurements of quantum level energies in molecular systems provide a test ground for new physics, as such effects could manifest themselves as minute shifts in the quantum level structures of atoms and molecules. For the…
In this paper, we introduce a novel approach to solve the many-body Schrodinger equation by the tensor neural network. Based on the tensor product structure, we can do the direct numerical integration by using fixed quadrature points for…
The Schrodinger equation has been considered to be a postulate of quantum physics, but it is also perceived and derived heuristically as the quantum equivalent of the classical energy relation. We indicate that the Schrodinger equation…
We develop a formalism to directly evaluate the matrix of force constants within a Quantum Monte Carlo calculation. We utilize the matrix of force constants to accurately relax the positions of atoms in molecules and determine their…
Nonrelativistic collision of proton and antiproton with hydrogen atom described by solving time-dependent Schrodinger equation numerically. Coulomb wave function discrete variable method (CWDVR) had been used to calculate electron wave…