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

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.

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