Exact solvable model for the Stark effect on a hydrogen atom

1986 ◽  
Vol 54 (6) ◽  
pp. 565-567
Author(s):  
Jan Makarewicz
Keyword(s):  
Hydrogen Atom ◽  
Stark Effect ◽  
Solvable Model

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

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

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 IN A FINITE REGION FOR A 1D COULOMB POTENTIAL

2002 ◽  
Vol 09 (05n06) ◽  
pp. 1827-1830 ◽  
Author(s):  
G. J. VÁZQUEZ ◽  
C. AVENDAÑO ◽  
J. A. REYES ◽  
M. DEL CASTILLO-MUSSOT ◽  
H. SPECTOR
Keyword(s):  
Hydrogen Atom ◽  
Analytical Solution ◽  
Electric Field ◽  
Stark Effect ◽  
Strong Field ◽  
Strong Electric Field ◽  
Electronic States ◽  
Finite Region ◽  
Electric Field Effects ◽  
One Dimensional

We calculate the states of a one-dimensional hydrogen atom under the effect of an electric field (Stark effect) in the strong field regime being the field confined in a finite region of width 2a (capacitor region). We find numerically the solution inside the capacitor and match it to an analytical solution outside the capacitor. Although the electric field tends to separate the two opposite charges particles, the total energy of the system decreases with increasing electric field strength. Our results are useful as a guideline to study strong electric field effects in electronic states of impurities or excitons in 1D systems.

scholarly journals LAMB SHIFT AND STARK EFFECT IN SIMULTANEOUS SPACE–SPACE AND MOMENTUM–MOMENTUM NONCOMMUTATIVE QUANTUM MECHANICS AND θ-DEFORMED su(2) ALGEBRA

2007 ◽  
Vol 22 (05) ◽  
pp. 377-383 ◽  
Author(s):  
S. A. ALAVI
Keyword(s):  
Quantum Mechanics ◽  
Hydrogen Atom ◽  
Lamb Shift ◽  
Stark Effect ◽  
Identical Particles ◽  
Noncommutative Quantum Mechanics ◽  
The One ◽  
Noncommutative Quantum

We study the spectrum of hydrogen atom, Lamb shift and Stark effect in the framework of simultaneous space–space and momentum–momentum (s-s, p-p) noncommutative quantum mechanics. The results show that the widths of Lamb shift due to noncommutativity is bigger than the one presented in Ref. 1. We also study the algebras of observables of systems of identical particles in s-s, p-p noncommutative quantum mechanics. We introduce θ-deformed su(2) algebra.

Dispersion relations for the stark effect in the hydrogen atom

1979 ◽  
Vol 71 (2-3) ◽  
pp. 197-200 ◽  
Author(s):  
S.C. Kanavi ◽  
C.H. Mehta ◽  
S.H. Patil
Keyword(s):  
Hydrogen Atom ◽  
Stark Effect ◽  
Dispersion Relations
Sign in / Sign up

Export Citation Format

Share Document