Approximate solutions to the quantum problem of two opposite charges in a constant magnetic field

J S ARDENGHI; M GADELLA; J NEGRO

PHYSICS LETTERS A

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2016 vol. 380 p. 1817 - 1823

0375-9601

We consider two particles of equal mass and opposite charge in a plane subject to a perpendicularconstant magnetic field. This system is integrable but not superintegrable. From the quantum point ofview, the solution is given by two fourth degree Hill differential equations which involve the energy aswell as a second constant of motion. There are two solvable approximations in relation to the value of aparameter. Starting from each of these approximations, a consistent perturbation theory can be appliedto get approximate values of the energy levels and of the second constant of motion.