Compression effects on dipole transitions and state lifetimes for a hydrogen atom

2016 ◽  
Vol 94 (9) ◽  
pp. 894-901 ◽  
Author(s):  
A. Solórzano ◽  
N. Aquino ◽  
A. Flores-Riveros
Keyword(s):  
Boundary Condition ◽  
Hydrogen Atom ◽  
Excited States ◽  
Dirichlet Boundary ◽  
Numerical Technique ◽  
Oscillator Strengths ◽  
Quantum Mechanical ◽  
Mechanical Problem ◽  
Radial Schrödinger Equation ◽  
Compression Effects

The quantum mechanical problem of a hydrogen atom placed at the center of an impenetrable sphere of radius r0 is solved by using two different methods, where, in the first, a trial wave function, consisting of a hydrogen-like function times a cutoff factor that ensures fulfillment of Dirichlet boundary condition, is proposed, whereas in the second, the radial Schrödinger equation is solved by means of an accurate numerical technique. We computed the energies for the ground and first excited states of S-, P-, and D-symmetry, as well as dipole transitions, oscillator strengths, and a few state lifetimes. Although the variational method and the numerical solution are found to give similar qualitative behaviours, which, in general, compare reasonably well with some results published previously, the 2p state lifetimes obtained in the present calculations appear to be at variance with the latter at some particular box radii.

Numerical Study of Periodic Traveling Wave Solutions for the Predator–Prey Model with Landscape Features

2015 ◽  
Vol 25 (09) ◽  
pp. 1550117 ◽  
Author(s):  
Ana Yun ◽  
Jaemin Shin ◽  
Yibao Li ◽  
Seunggyu Lee ◽  
Junseok Kim
Keyword(s):  
Boundary Condition ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Dirichlet Boundary ◽  
Numerical Technique ◽  
Traveling Wave Solutions ◽  
Predator Prey ◽  
Landscape Features ◽  
Wave Solutions ◽  
Periodic Traveling Wave

We numerically investigate periodic traveling wave solutions for a diffusive predator–prey system with landscape features. The landscape features are modeled through the homogeneous Dirichlet boundary condition which is imposed at the edge of the obstacle domain. To effectively treat the Dirichlet boundary condition, we employ a robust and accurate numerical technique by using a boundary control function. We also propose a robust algorithm for calculating the numerical periodicity of the traveling wave solution. In numerical experiments, we show that periodic traveling waves which move out and away from the obstacle are effectively generated. We explain the formation of the traveling waves by comparing the wavelengths. The spatial asynchrony has been shown in quantitative detail for various obstacles. Furthermore, we apply our numerical technique to the complicated real landscape features.

scholarly journals Oscillator Representation and Generalized van der Waals Hamiltonians

1997 ◽  
Vol 12 (16) ◽  
pp. 1193-1207
Author(s):  
M. Dineykhan
Keyword(s):  
Hydrogen Atom ◽  
Excited States ◽  
Ground State ◽  
Van Der Waals ◽  
Bound State ◽  
Oscillator Strengths ◽  
Uniform Electric Field ◽  
Oscillator Representation ◽  
Representation Method ◽  
Oscillator Representation Method

The oscillator representation method is extended to calculate the energy spectrum of bound state systems described by axially symmetrical potentials in the parabolic system coordinates. In particular, it is applied to calculate the energy of the ground and excited states of the hydrogen atom in the uniform electric field and van der Waals field. The method gives the perturbation formulas for the analytic spectrum of the hydrogen atom in the generalized van der Waals field and defines oscillator strengths for transitions from the ground state to the perturbed manifold n=10, m=0.

scholarly journals Role of the cut-off function for the ground state variational wavefunction of the hydrogen atom confined by a hard sphere

2019 ◽  
Vol 65 (2) ◽  
pp. 116 ◽  
Author(s):  
R.A. Rojas ◽  
And N. Aquino
Keyword(s):  
Boundary Condition ◽  
Hydrogen Atom ◽  
Ground State ◽  
Dirichlet Boundary Condition ◽  
Hard Sphere ◽  
Dirichlet Boundary ◽  
Variational Treatment ◽  
Exact Calculations ◽  
Cusp Condition

A variational treatment of the hydrogen atom in its ground state, enclosed by a hard spherical cavity of radius Rc , is developed by considering the ansatz wavefunction as the product of the free-atom 1s orbital times a cut-off function to satisfy the Dirichlet boundary condition imposed by the impenetrable confining sphere. Seven different expressions for the cut-off function are employed to evaluate the energy, the cusp condition, <r^-1>,<r>, <r^2>, and the Shannon entropy, and  as a function of Rc in each case. We investigate which of the proposed cut-off functions provides best agreement with available corresponding exact calculations for the above quantities. We find that most of these cut-off functions work better in certain regions of Rc , while others are identified to give bad results in general. The cut-off functions that give, on average, better results are of the form (1- (r/Rc)^n), n=1,2,3

Impulsive forces and the Heisenberg equations of motion for a particle in a box

1993 ◽  
Vol 71 (7-8) ◽  
pp. 380-388 ◽  
Author(s):  
W. A. Atkinson ◽  
M. Razavy
Keyword(s):  
Boundary Condition ◽  
Wave Function ◽  
Wave Equation ◽  
Equations Of Motion ◽  
Free Particle ◽  
Quantum Mechanical ◽  
Mechanical Problem ◽  
Impulsive Forces ◽  
Heisenberg Equations ◽  
Heisenberg Equations Of Motion

The quantum mechanical problem of a particle bouncing between two walls is formulated both in terms of the Heisenberg equations of motion and the Schrödinger equation. The reason for considering the Heisenberg equations is to understand the quantal nature of the impulsive forces. It is shown that these two formulations are compatible if, in addition to the classical impulsive forces, there are singular forces proportional to [Formula: see text] and [Formula: see text], i.e., forces of quantum origin. When these forces are added to the free-particle Hamiltonian then the total Hamiltonian is self-adjoint, and from it one can derive the boundary condition that must be imposed on the wave function. As an application of this formulation one can study the quantum mechanics of classical dynamical systems expressible as difference equations, e.g., the problem of a particle trapped between two walls moving relative to each other. The total Hamiltonian can also be used to study the question of the separability of the wave equation for such a motion.

scholarly journals On some classes of generalized Schrödinger equations

2020 ◽  
Vol 10 (1) ◽  
pp. 522-533
Author(s):  
Amanda S. S. Correa Leão ◽  
Joelma Morbach ◽  
Andrelino V. Santos ◽  
João R. Santos Júnior
Keyword(s):  
Boundary Condition ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Laplacian Operator ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nontrivial Solutions ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Stationary Problems

Abstract Some classes of generalized Schrödinger stationary problems are studied. Under appropriated conditions is proved the existence of at least 1 + $\begin{array}{} \sum_{i=2}^{m} \end{array}$ dim Vλi pairs of nontrivial solutions if a parameter involved in the equation is large enough, where Vλi denotes the eigenspace associated to the i-th eigenvalue λi of laplacian operator with homogeneous Dirichlet boundary condition.

scholarly journals Quantum-mechanical hydration plays critical role in the stability of firefly oxyluciferin isomers: State-of-the-art calculations of the excited states

2020 ◽  
Vol 153 (20) ◽  
pp. 201103
Author(s):  
Yoshifumi Noguchi ◽  
Miyabi Hiyama ◽  
Motoyuki Shiga ◽  
Hidefumi Akiyama ◽  
Osamu Sugino
Keyword(s):  
Excited States ◽  
State Of The Art ◽  
Critical Role ◽  
Quantum Mechanical ◽  
The Stability
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