Monolayer phosphorene under time-dependent magnetic field

We obtain the exact wave function of a monolayer phosphorene under a low- intensity time-dependent magnetic field using the dynamical invariant method. We calculate the quantum-mechanical energy expectation value and the transition probability for a constant and an oscillatory magnetic field. For the former we observe that the Landau level energy varies linearly with the quantum numbers n and m and the magnetic field intensity B_0. No transition takes place. For the latter, we observe that the energy oscillates in time, increasing linearly with the Landau level n and m and nonlinearly with the magnetic field. The (k,l) to (n,m) transitions take place only for l=m. We investigate the (0,0) to (n,0) and (1,l) and (2,l) probability transitions.