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.

scholarly journals Noncommutative Phase Space Schrödinger Equation with Minimal Length

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
H. Hassanabadi ◽  
Z. Molaee ◽  
S. Zarrinkamar
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
External Magnetic Field ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Jacobi Polynomials ◽  
Minimal Length ◽  
Two Dimensional ◽  
Noncommutative Phase Space ◽  
Energy Eigenvalues

We consider the Schrödinger equation under an external magnetic field in two-dimensional noncommutative phase space with an explicit minimal length relation. The eigenfunctions are reported in terms of the Jacobi polynomials, and the explicit form of energy eigenvalues is reported.

SPATIOTEMPORAL PATTERNS IN LANGMUIR PLASMAS

1994 ◽  
Vol 08 (24) ◽  
pp. 1503-1510 ◽  
Author(s):  
CANGTAO ZHOU ◽  
X.T. HE
Keyword(s):  
Phase Space ◽  
Schrödinger Equation ◽  
Spatial Patterns ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Numerical Results ◽  
Spatiotemporal Patterns ◽  
Two Dimensional ◽  
Fourier Space ◽  
Quintic Nonlinear Schrödinger Equation

The constitutions of the phase space, stochasticity, and the complicated patterns of Langmuir fields are investigated in terms of a two-dimensional cubic-quintic nonlinear Schrödinger equation. The numerical results obviously illustrate that the quintic non-linearity leads to the production of the complicated patterns. The mechanism to form these spatial patterns is also analyzed by measuring the spectrum of energy in Fourier space. It is shown that the complicated patterns are associated with the complexity of trajectory in phase space and the stochastic partition of energy in Fourier modes.

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