Related papers: General Quantization Rule
Given a spatially dependent mass distribution we obtain potential functions for exactly solvable nonrelativistic problems. The energy spectrum of the bound states and their wavefunctions are written down explicitly. This is accomplished by…
Physical research looks for clues to quantum properties of the gravitational field. On the basis of the common Schr\"odinger theory, a simple model of the quantization of a Friedmann universe comprising dust and radiation is investigated.…
In quantum theory, bound states are described by eigenvalue equations, which usually cannot be solved exactly. However, some simple general theorems allow to derive rigorous statements about the corresponding solutions, that is, energy…
Quantum mechanics has about a dozen exactly solvable potentials. Normally, the time-independent Schroedinger equation for them is solved by using a generalized series solution for the bound states (using the Froebenius method) and then an…
Two approaches to quantization of Freedman's closed Universe are compared. In the first approach, the Shrodinger's norm of the wave function of Universe is used, and in the second approach, the Klein-Gordon's norm is used. The second one…
Spectroscopic techniques are very essential tools in studying electronic structures, spectroscopic constants and energetic properties of diatomic molecules. These techniques are also required for parametrization of new method based on…
We obtain the spectrum of bound states for a modified P\"oschl-Teller and square potential wells in the nonlinear Schr\"odinger equation. For a fixed norm of bound states, the spectrum for both potentials turns out to consist of a finite…
Exact solution of Schrodinger equation for the Mie potential is obtained for an arbitrary angular momentum. The energy eigenvalues and the corresponding wavefunctions are calculated by the use of the Nikiforov-Uvarov method. Wavefunctions…
We use the Bohr-Sommerfeld quantization approach in the context of constituent quark models. This method provides, for the Cornell potential, analytical formulae for the energy spectra which closely approximate numerical exact calculations…
An infinite sequence of potential well functions is considered. A trial wavefunction is used with the Schr$\ddot{\text{o}}$dinger equation to obtain an approximate ground state energy for each potential well function. We obtain an…
Polarizability is a key response property of physical and chemical systems, which has an impact on intermolecular interactions, spectroscopic observables, and vacuum polarization. The calculation of polarizability for quantum systems…
Elementary introduction to the application of Mathematica 3.0 to the solution of bound-state problems in quantum theory by standard variational procedures, with particular emphasis on the computation of precise upper bounds on energy levels…
In this study, we employ exact quantization rule (EQR) to derive the analytical approximate l-wave solutions of the Schrodinger equation with the general molecular oscillator (GMO). The energy eigenvalues equation and the corresponding wave…
The stationary 1D Schr\"odinger equation with a polynomial potential $V(q)$ of degree N is reduced to a system of exact quantization conditions of Bohr-Sommerfeld form. They arise from bilinear (Wronskian) functional relations pairing…
Using a hydrogen molecule as a test system we demonstrate how to compute the effective potential according to the formalism of the new density functional theory (DFT), in which the basic variable is the set of spherically averaged densities…
The polynomial solution of the Schrodinger equation for the Pseudoharmonic potential is found for any arbitrary angular momentum $l$. The exact bound-state energy eigenvalues and the corresponding eigen functions are analytically…
We focus on a recently developed generalized pseudospectral method for accurate, efficient treatment of certain central potentials of interest in various branches in quantum mechanics, usually having singularity. Essentially this allows…
In this thesis, we study a quantization condition in relation to the solvability of Schr\"{o}dinger equations. This quantization condition is called the SWKB (supersymmetric Wentzel-Kramers-Brillouin) quantization condition and has been…
We summarise and discuss some of our previous results, which show that Bohr's theory of the one-electron atom may be derived from the theory underpinning Quantum ElectroDynamics (QED) or vice versa, and that General Relativity may also be…
Grothendieck's bound is used in the context of a single quantum system, in contrast to previous work which used it for multipartite entangled systems and the violation of Bell-like inequalities. Roughly speaking the Grothendieck theorem…