Effects of a non-Hermitian potential on the Landau quantization

2019 ◽  
Vol 34 (12) ◽  
pp. 1950072 ◽  
Author(s):  
B. F. Ramos ◽  
I. A. Pedrosa ◽  
K. Bakke
Keyword(s):  
Magnetic Field ◽  
Energy Spectrum ◽  
Schrödinger Equation ◽  
Complex Potential ◽  
Schrodinger Equation ◽  
Uniform Magnetic Field ◽  
Spinless Particle ◽  
Symmetric Complex

In this work, we solve the time-independent Schrödinger equation for a Landau system modulated by a non-Hermitian Hamiltonian. The system consists of a spinless particle in a uniform magnetic field submitted to action of a non-[Formula: see text] symmetric complex potential. Although the Hamiltonian is neither Hermitian nor [Formula: see text]-symmetric, we find that the Landau problem under study exhibits an entirely real energy spectrum.

The solution of the Schrödinger equation for finite systems, with special reference to the motion of electrons in Coulomb electric fields and uniform magnetic fields

1953 ◽  
Vol 49 (1) ◽  
pp. 103-114 ◽  
Author(s):  
R. B. Dingle
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Schrödinger Equation ◽  
Special Reference ◽  
Electric Fields ◽  
Schrodinger Equation ◽  
Uniform Magnetic Field ◽  
Coulomb Field ◽  
Finite Systems ◽  
Finite Extent

ABSTRACTA number of methods are formulated for solving the Schrödinger equation for systems of finite extent. The methods are developed in detail for the particular case of an electron moving in a Coulomb field (e.g. hydrogen-like atom), with a boundary consisting of a sphere of given radius. In the second part of the paper these results are transformed into those for an electron moving in a uniform magnetic field, the boundary of the system being cylindrical.

scholarly journals WIGNER FUNCTIONS FOR THE LANDAU PROBLEM IN NONCOMMUTATIVE SPACES

2002 ◽  
Vol 17 (29) ◽  
pp. 1937-1944 ◽  
Author(s):  
ÖMER F. DAYI ◽  
LARA T. KELLEYANE
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Uniform Magnetic Field ◽  
Effective Hamiltonian ◽  
Wigner Functions ◽  
Noncommutative Spaces

An electron moving on plane in a uniform magnetic field orthogonal to the plane is known as the Landau problem. Wigner functions for the Landau problem when the plane is noncommutative are found employing solutions of the Schrödinger equation as well as solving the ordinary ⋆-genvalue equation in terms of an effective Hamiltonian. Then, we let momenta and coordinates of the phase space be noncommutative and introduce a generalized ⋆-genvalue equation. We solve this equation to find the related Wigner functions and show that under an appropriate choice of noncommutativity relations they are independent of noncommutativity parameter.

Study of Schrödinger equation in terms of Heun functions in the commutative vs. non-commutative spaces

2019 ◽  
Vol 34 (23) ◽  
pp. 1950183 ◽  
Author(s):  
S. Sargolzaeipor ◽  
H. Hassanabadi ◽  
W. S. Chung
Keyword(s):  
Magnetic Field ◽  
Energy Spectrum ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Wave Functions ◽  
Heun Functions ◽  
Commutative Space

In this paper, we solved the Schrödinger equation in the commutative and non-commutative (NC) spaces under the presence of magnetic field. In other words, we obtained the energy spectrum and wave functions in terms of Heun functions. When we considered the case [Formula: see text], we observed that the NC space converts to the commutative space.

LANDAU LEVELS IN METALS—A PHYSICAL ANALOGUE

1967 ◽  
Vol 45 (6) ◽  
pp. 2015-2020
Author(s):  
P. L. Taylor
Keyword(s):  
Magnetic Field ◽  
Simple Model ◽  
Schrödinger Equation ◽  
Conduction Electron ◽  
Schrodinger Equation ◽  
Uniform Magnetic Field ◽  
Physical Problem ◽  
Landau Levels ◽  
Approximate Description

The Schrödinger equation is considered for a simple model of a conduction electron in a uniform magnetic field. It is shown how this equation may be transformed into an approximate description of a different and simpler physical problem, from which the usual semiclassical results may be derived.

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