Variable scaling method and the Stark effect in the hydrogen atom

1985 ◽  
Vol 63 (9) ◽  
pp. 1212-1214
Author(s):  
R. K. Roychoudhury ◽  
Barnana Roy
Keyword(s):  
Hydrogen Atom ◽  
Stark Effect ◽  
Anharmonic Oscillator ◽  
Laguerre Polynomials ◽  
Numerical Results ◽  
Optimal Solutions ◽  
Matrix Elements ◽  
Scaling Method ◽  
Energy Eigenvalues

By relating the Stark-effect problem in hydrogenlike atoms to that of the spherical anharmonic oscillator, we have found simple formulae for energy eigenvalues for the Stark effect. Matrix elements have been calculated using the properties of Laguerre polynomials, and then the variable scaling method has been used to find optimal solutions. Our numerical results are compared with those of Hioe and Yoo and also with the results obtained by Lanczos.

Stark effect for a confined hydrogen atom

1981 ◽  
Vol 14 (24) ◽  
pp. 4737-4742 ◽  
Author(s):  
M Friedman ◽  
A Rabinovitch ◽  
R Thieberger
Keyword(s):  
Hydrogen Atom ◽  
Stark Effect

Dirac equation with multiparameter-potential and Hulthén tensor interaction under relativistic symmetries

Open Physics ◽  
2014 ◽  
Vol 12 (12) ◽  
Author(s):  
Sami Ortakaya
Keyword(s):  
Dirac Equation ◽  
Spin Symmetry ◽  
Tensor Interaction ◽  
Numerical Results ◽  
Exponential Potential ◽  
Energy Eigenvalues ◽  
Nu Method

AbstractThe pseudospin and spin symmetric solutions of the Dirac equation with Hulthén-type tensor interaction are obtained under multi-parameter-exponential potential (MEP) for arbitrary κ states. The energy eigenvalues and the corresponding eigenfunctions are also obtained using the parametric Nikiforov-Uvarov (NU) method. Some numerical results are also obtained for pseudospin and spin symmetry limits.

scholarly journals THE ENERGY EIGENVALUES OF THE TWO DIMENSIONAL HYDROGEN ATOM IN A MAGNETIC FIELD

2006 ◽  
Vol 15 (06) ◽  
pp. 1263-1271 ◽  
Author(s):  
A. SOYLU ◽  
O. BAYRAK ◽  
I. BOZTOSUN
Keyword(s):  
Magnetic Field ◽  
Hydrogen Atom ◽  
Iteration Method ◽  
Weak Magnetic Field ◽  
The Other ◽  
Asymptotic Iteration Method ◽  
Iterative Approach ◽  
Two Dimensional ◽  
Energy Eigenvalues ◽  
The Magnetic Field

In this paper, the energy eigenvalues of the two dimensional hydrogen atom are presented for the arbitrary Larmor frequencies by using the asymptotic iteration method. We first show the energy eigenvalues for the case with no magnetic field analytically, and then we obtain the energy eigenvalues for the strong and weak magnetic field cases within an iterative approach for n=2-10 and m=0-1 states for several different arbitrary Larmor frequencies. The effect of the magnetic field on the energy eigenvalues is determined precisely. The results are in excellent agreement with the findings of the other methods and our method works for the cases where the others fail.

Multipole matrix elements for hydrogen atom

1991 ◽  
Vol 44 (2) ◽  
pp. 154-157 ◽  
Author(s):  
Akira Matsumoto
Keyword(s):  
Hydrogen Atom ◽  
Matrix Elements

scholarly journals The stark effect of the fine-structure of hydrogen

1928 ◽  
Vol 119 (782) ◽  
pp. 313-334 ◽  
Keyword(s):  
Fine Structure ◽  
Hydrogen Atom ◽  
Electric Field ◽  
Quantum Dynamics ◽  
Stark Effect ◽  
Energy Levels ◽  
Structure Theory ◽  
Weak Electric Field ◽  
Classical Dynamics ◽  
Balmer Series

One of the earliest successes of classical quantum dynamics in a field where ordinary methods had proved inadequate was the solution, by Schwarzschild and Epstein, of the problem of the hydrogen atom in an electric field. It was shown by them that under the influence of the electric field each of the energy levels in which the unperturbed atom can exist on Bohr’s original theory breaks up into a number of equidistant levels whose separation is proportional to the strength of the field. Consequently, each of the Balmer lines splits into a number of components with separations which are integral multiples of the smallest separation. The substitution of the dynamics of special relativity for classical dynamics in the problem of the unperturbed hydrogen atom led Sommerfeld to his well-known theory of the fine-structure of the levels; thus, in the absence of external fields, the state n = 1 ( n = 2 in the old notation) is found to consist of two levels very close together, and n = 2 of three, so that the line H α of the Balmer series, which arises from a transition between these states, has six fine-structure components, of which three, however, are found to have zero intensity. The theory of the Stark effect given by Schwarzschild and Epstein is adequate provided that the electric separation is so much larger than the fine-structure separation of the unperturbed levels that the latter may be regarded as single; but in weak fields, when this is no longer so, a supplementary investigation becomes necessary. This was carried out by Kramers, who showed, on the basis of Sommerfeld’s original fine-structure theory, that the first effect of a weak electric field is to split each fine-structure level into several, the separation being in all cases proportional to the square of the field so long as this is small. When the field is so large that the fine-structure is negligible in comparison with the electric separation, the latter becomes proportional to the first power of the field, in agreement with Schwarzschild and Epstein. The behaviour of a line arising from a transition between two quantum states will be similar; each of the fine-structure components will first be split into several, with a separation proportional to the square of the field; as the field increases the separations increase, and the components begin to perturb each other in a way which leads ultimately to the ordinary Stark effect.

The Stark effect on an excited hydrogen atom

1983 ◽  
Vol 51 (7) ◽  
pp. 610-612 ◽  
Author(s):  
C. Barratt
Keyword(s):  
Hydrogen Atom ◽  
Stark Effect

THE ASYMPTOTIC ITERATION METHOD FOR THE EIGENENERGIES OF THE ASYMMETRICAL QUANTUM ANHARMONIC OSCILLATOR POTENTIALS $V(x)=\sum_{j=2}^{2\alpha}A_{j}x^{j}$

2007 ◽  
Vol 22 (01) ◽  
pp. 203-212 ◽  
Author(s):  
T. BARAKAT ◽  
O. M. AL-DOSSARY
Keyword(s):  
Rate Of Convergence ◽  
Iteration Method ◽  
Anharmonic Oscillator ◽  
Full Range ◽  
Adjustable Parameter ◽  
Numerical Results ◽  
Asymptotic Iteration Method ◽  
Anharmonic Oscillators ◽  
Parameter Values

The asymptotic iteration method is used to calculate the eigenenergies for the asymmetrical quantum anharmonic oscillator potentials [Formula: see text], with (α = 2) for quartic, and (α = 3) for sextic asymmetrical quantum anharmonic oscillators. An adjustable parameter β is introduced in the method to improve its rate of convergence. Comparing the present results with the exact numerical values, and with the numerical results of the earlier works, it is found that asymptotically, this method gives accurate results over the full range of parameter values Aj.

Sign in / Sign up

Export Citation Format

Share Document