Ground State of the One-Dimensional Hydrogen Atom

1966 ◽  
Vol 34 (12) ◽  
pp. 1194-1195 ◽  
Author(s):  
M. Andrews
Keyword(s):  
Hydrogen Atom ◽  
Ground State ◽  
One Dimensional ◽  
The One

scholarly journals One-dimensional hydrogen atom

2016 ◽  
Vol 472 (2185) ◽  
pp. 20150534 ◽  
Author(s):  
Rodney Loudon
Keyword(s):  
Hydrogen Atom ◽  
Schrödinger Equation ◽  
Ground State ◽  
Short Distance ◽  
Schrodinger Equation ◽  
Three Dimensional ◽  
One Dimension ◽  
Current Status ◽  
One Dimensional ◽  
The One

The theory of the one-dimensional (1D) hydrogen atom was initiated by a 1952 paper but, after more than 60 years, it remains a topic of debate and controversy. The aim here is a critique of the current status of the theory and its relation to relevant experiments. A 1959 solution of the Schrödinger equation by the use of a cut-off at x = a to remove the singularity at the origin in the 1/| x | form of the potential is clarified and a mistaken approximation is identified. The singular atom is not found in the real world but the theory with cut-off has been applied successfully to a range of four practical three-dimensional systems confined towards one dimension, particularly their observed large increases in ground state binding energy. The true 1D atom is in principle restored when the short distance a tends to zero but it is sometimes claimed that the solutions obtained by the limiting procedure differ from those obtained by solution of the basic Schrödinger equation without any cut-off in the potential. The treatment of the singularity by a limiting procedure for applications to practical systems is endorsed.

scholarly journals Unusually kicked dynamics: Hydrogen atom in a spherical box

Open Physics ◽  
2012 ◽  
Vol 10 (4) ◽  
Author(s):  
Dragoslav Mašović
Keyword(s):  
Hydrogen Atom ◽  
Excited States ◽  
Ground State ◽  
Laser Pulses ◽  
Ionization Probability ◽  
Positive Energy ◽  
Rabi Oscillations ◽  
One Dimensional ◽  
The Real ◽  
The One

AbstractIn this paper we have examined the ionization of the ground state hydrogen atom in a spherical box with laser pulses of specific shapes. These shapes are predicted assuming correspondence under some conditions with the alternating kicking field. Unusually kicked dynamics is suggested. It is shown that such kicked dynamics leads to generalized Rabi oscillations with the positive energy states included and participation of the excited states. The correspondence with the real pulse is established emphasizing such unusually kicked dynamics. The approach is verified on the one-dimensional (1D) hydrogen atom and calculation of the known results for ionization probability.

Dimer Character of the Ground State of the One Dimensional t-J-J' Model

1993 ◽  
Vol 62 (2) ◽  
pp. 834-834
Author(s):  
Kazuhiro Sano ◽  
Ken'ichi Takano
Keyword(s):  
Ground State ◽  
One Dimensional ◽  
The One
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