Neural network solution of the Schrödinger equation for a two-dimensional harmonic oscillator

1993 ◽  
Vol 173 (3) ◽  
pp. 377-383 ◽  
Author(s):  
J. Androsiuk ◽  
L. Kułak ◽  
K. Sienicki
Keyword(s):  
Neural Network ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Two Dimensional ◽  
Network Solution

scholarly journals Deep-neural-network solution of the electronic Schrödinger equation

2020 ◽  
Vol 12 (10) ◽  
pp. 891-897 ◽  
Author(s):  
Jan Hermann ◽  
Zeno Schätzle ◽  
Frank Noé
Keyword(s):  
Neural Network ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Deep Neural Network ◽  
Network Solution

scholarly journals Zeeman Effect in Phase Space

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
R. A. S. Paiva ◽  
R. G. G. Amorim ◽  
S. C. Ulhoa ◽  
A. E. Santana ◽  
F. C. Khanna
Keyword(s):  
Magnetic Field ◽  
Perturbation Theory ◽  
Phase Space ◽  
External Magnetic Field ◽  
Hydrogen Atom ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Zeeman Effect ◽  
Two Dimensional

The two-dimensional hydrogen atom in an external magnetic field is considered in the context of phase space. Using the solution of the Schrödinger equation in phase space, the Wigner function related to the Zeeman effect is calculated. For this purpose, the Bohlin mapping is used to transform the Coulomb potential into a harmonic oscillator problem. Then, it is possible to solve the Schrödinger equation easier by using the perturbation theory. The negativity parameter for this system is realised.

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