On square-integrability of solutions of the stationary Schrödinger equation for the quantum harmonic oscillator in two dimensional constant curvature spaces

2015 ◽  
Vol 56 (7) ◽  
pp. 072101 ◽  
Author(s):  
Norman Noguera ◽  
Krzysztof Rózga
Keyword(s):  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Constant Curvature ◽  
Schrodinger Equation ◽  
Two Dimensional ◽  
Quantum Harmonic Oscillator ◽  
Stationary Schrödinger Equation ◽  
Square Integrability ◽  
Constant Curvature Spaces

scholarly journals Discrete Quantum Harmonic Oscillator

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1362
Author(s):  
Alina Dobrogowska ◽  
David J. Fernández C.
Keyword(s):  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Discrete Model ◽  
Schrodinger Equation ◽  
Factorization Method ◽  
Quantum Harmonic Oscillator ◽  
Meixner Polynomials

In this paper, we propose a discrete model for the quantum harmonic oscillator. The eigenfunctions and eigenvalues for the corresponding Schrödinger equation are obtained through the factorization method. It is shown that this problem is also connected with the equation for Meixner polynomials.

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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