Schrödinger equation in two dimensions for a zero‐range potential and a uniform magnetic field: An exactly solvable model

1991 ◽  
Vol 59 (1) ◽  
pp. 52-54 ◽  
Author(s):  
J. Fernando Perez ◽  
F. A. B. Coutinho
Keyword(s):  
Magnetic Field ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Uniform Magnetic Field ◽  
Solvable Model ◽  
Two Dimensions ◽  
Exactly Solvable Model ◽  
Range Potential ◽  
Exactly Solvable ◽  
Zero Range

scholarly journals A quasi-exactly solvable model: Two charges in a magnetic field subject to a non-Coulomb mutual interaction

2015 ◽  
Vol 29 (29) ◽  
pp. 1550204
Author(s):  
Michael Kreshchuk
Keyword(s):  
Magnetic Field ◽  
Exact Solutions ◽  
Coulomb Interaction ◽  
Differential Form ◽  
Uniform Magnetic Field ◽  
Solvable Model ◽  
Mutual Interaction ◽  
Planar Motion ◽  
Exactly Solvable Model ◽  
Exactly Solvable

In this paper, we extend the class of QM problems which permit for quasi-exact solutions. Specifically, we consider planar motion of two interacting charges in a constant uniform magnetic field. While Turbiner and Escobar–Ruiz (2013) addressed the case of the Coulomb interaction between the particles, we explore three other potentials. We do this by reducing the appropriate Hamiltonians to the second-order polynomials in the generators of the representation of SL(2, C) group in the differential form. This allows us to perform partial diagonalization of the Hamiltonian and to reduce the search for the first few energies and the corresponding wavefunctions to an algebraic procedure.

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.

scholarly journals Exactly solvable model of three interacting particles in an external magnetic field

2003 ◽  
Vol 67 (20) ◽  
Author(s):  
E. P. Nakhmedov ◽  
K. Morawetz ◽  
M. Ameduri ◽  
A. Yurtsever ◽  
C. Radehaus
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Solvable Model ◽  
Interacting Particles ◽  
Exactly Solvable Model ◽  
Exactly Solvable
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