Exact solutions of ann-dimensional anisotropic oscillator in a uniform magnetic field

1972 ◽  
Vol 7 (2) ◽  
pp. 265-276 ◽  
Author(s):  
E. E. Bergmann ◽  
A. Holz
Keyword(s):  
Magnetic Field ◽  
Exact Solutions ◽  
Uniform Magnetic Field ◽  
Anisotropic Oscillator

scholarly journals The exact solutions of a (2 + 1)-dimensional Dirac oscillator under a magnetic field in the presence of a minimal length

2015 ◽  
Vol 93 (5) ◽  
pp. 542-548 ◽  
Author(s):  
Abdelmalek Boumali ◽  
Hassan Hassanabadi
Keyword(s):  
Magnetic Field ◽  
Exact Solutions ◽  
Momentum Space ◽  
Uniform Magnetic Field ◽  
Hypergeometric Functions ◽  
Minimal Length ◽  
Wave Functions ◽  
Two Dimensional ◽  
Dirac Oscillator ◽  
Energy Eigenvalues

Minimal length of a two-dimensional Dirac oscillator is investigated in the presence of a uniform magnetic field and illustrates the wave functions in the momentum space. The energy eigenvalues are found and the corresponding wave functions are calculated in terms of hypergeometric functions.

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.

Surface of a magnetic fluid containing magnetizable bodies in an applied uniform magnetic field

2008 ◽  
Vol 44 (2) ◽  
pp. 175-182 ◽  
Author(s):  
K. Zimmermann ◽  
V.A. Naletova ◽  
I. Zeidis ◽  
V.A. Turkov ◽  
D.A. Pelevina ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Magnetic Fluid ◽  
Uniform Magnetic Field
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