PERTURBED WAVEFUNCTIONS OF THE EXCITED STATES OF HYDROGEN ATOM IN STARK EFFECT

1994 ◽  
Vol 08 (06) ◽  
pp. 727-740 ◽  
Author(s):  
G. K. SAPRA ◽  
V. S. BHASIN ◽  
L. S. KOTHARI
Keyword(s):  
Hydrogen Atom ◽  
Electric Field ◽  
External Electric Field ◽  
Excited States ◽  
Ground State ◽  
Stark Effect ◽  
Second Order ◽  
Electric Polarizability ◽  
Perturbation Equations

We extend the procedure originally suggested by Dalgarno and Lewis in studying the second-order Stark effect for the ground-state hydrogen atom to the excited states. We solve the perturbation equations for the excited states of hydrogen atom placed in an external electric field to obtain expressions for the perturbed wavefunctions. Here the emphasis is on studying in detail the nature of the perturbed wavefunction rather than energy shifts as investigated in most of the attempts made so far. The effect of the electric field on these wavefunctions is analysed and the values of the electric polarizability of the hydrogen atom in the excited states obtained in this way are compared with the earlier work.

scholarly journals The Role of Polarizabilities in the Fluorescence Behaviour of 4-cyano-N,N-dimethylaniline

1981 ◽  
Vol 36 (8) ◽  
pp. 868-875 ◽  
Author(s):  
Wolfram Baumann
Keyword(s):  
Dipole Moment ◽  
Electric Field ◽  
External Electric Field ◽  
Ground State ◽  
Permanent Dipole Moment ◽  
Reaction Field

Abstract The effect of an external electric field on the absorption and the double fluorescence of 4-cyano-N,N-dimethylaniline can be understood, taking into account reaction field induced polarizability effects. If a TICT state conformation emits the a-fiuorescence in dioxane, the permanent dipole moment in this state is only slightly larger than in the equilibrium ground state.

Ein Level-Crossing-Experiment im angeregten (5p1/2 5d5/2)J=2-Term des Sn I zur Untersuchung der Energieverschiebungen im elektrischen Feld / Level-Crossing Experiment in the Excited (5p1/25d5/2)J=2-State of the Sn I for the Investigation of the Energy Shifts in an Electric Field

1970 ◽  
Vol 25 (5) ◽  
pp. 608-611
Author(s):  
P. Zimmermann
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Stark Effect ◽  
Second Order ◽  
Wave Functions ◽  
Zero Field ◽  
Homogeneous Electric Field ◽  
Level Crossing ◽  
Crossing Experiment ◽  
The Magnetic Field

Observing the change of the Hanle effect under the influence of a homogeneous electric field E the Stark effect of the (5p1/25d5/2)j=2-state in Sn I was studied. Due to the tensorial part β Jz2E2 in the Hamiltonian of the second order Stark effect the signal of the zero field crossing (M ∓ 2, M′ = 0 β ≷ 0 ) is shifted to the magnetic field H with gJμBH=2 | β | E2. From these shifts for different electric field strengths the value of the Stark parameter|β| = 0.21(2) MHz/(kV/cm)2 · gJ/1.13was deduced. A theoretical value of ß using Coulomb wave functions is discussed.

scholarly journals The hydrogen atom in plasmas with an external electric field

2014 ◽  
Vol 21 (9) ◽  
pp. 092703 ◽  
Author(s):  
M. K. Bahar ◽  
A. Soylu
Keyword(s):  
Hydrogen Atom ◽  
Electric Field ◽  
External Electric Field

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.

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.

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