The Noncommutative Landau Problem in Podolsky's Generalized Electrodynamics

The Landau problem in Podolsky's generalized electrodynamics is studied by the method of diagonalization in noncommutative phase space and we find that the different noncommutative effects for a certain system led by the nonuniqueness of generalized Bopp shift can be avoided. The exact energy eigenvalues are found, and the result shows that the energy spectra are generically non-degenerate. Furthermore, we obtain the special energy spectra of noncommutative space and commutative space.