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.

scholarly journals Supersymmetric Partners of the One-Dimensional Infinite Square Well Hamiltonian

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 350
Author(s):  
Manuel Gadella ◽  
José Hernández-Muñoz ◽  
Luis Miguel Nieto ◽  
Carlos San Millán
Keyword(s):  
Ground State ◽  
Infinite Sequence ◽  
Negative Energy ◽  
Transcendental Equation ◽  
The Self ◽  
Positive Energy ◽  
One Dimensional ◽  
Square Well ◽  
The One ◽  
Adjoint Operators

We find supersymmetric partners of a family of self-adjoint operators which are self-adjoint extensions of the differential operator −d2/dx2 on L2[−a,a], a>0, that is, the one dimensional infinite square well. First of all, we classify these self-adjoint extensions in terms of several choices of the parameters determining each of the extensions. There are essentially two big groups of extensions. In one, the ground state has strictly positive energy. On the other, either the ground state has zero or negative energy. In the present paper, we show that each of the extensions belonging to the first group (energy of ground state strictly positive) has an infinite sequence of supersymmetric partners, such that the ℓ-th order partner differs in one energy level from both the (ℓ−1)-th and the (ℓ+1)-th order partners. In general, the eigenvalues for each of the self-adjoint extensions of −d2/dx2 come from a transcendental equation and are all infinite. For the case under our study, we determine the eigenvalues, which are also infinite, all the extensions have a purely discrete spectrum, and their respective eigenfunctions for all of its ℓ-th supersymmetric partners of each extension.

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.

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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