Monocamada de fosforeno na presença de campo magnético dependente do tempo - Nascimento, João Pedro Gomes do (2019)
In this work we study electrons and holes in monolayer phosphorene under a low-intensity time-dependent magnetic field B(t). By considering B(t)=(0,0,B(t)) and choosing the symmetric gauge, A(r,t)=−(1/2)r x B(t), we use the Lewis and Riesenfeld method to obtain the wave functions for electrons and holes. From those solutions, we calculate the uncertainties, the Fisher information, the quantum-mechanical energy expectation value and the transition probabilities. We apply the results to the fields B(t)=B0k e B(t)=(B02+B12cos2(t))1/2k. The uncertainties for the ground state show squeezing phenomenon depending on the intensity of the oscillatory magnetic field. In this system, we also verify that the Fisher information provides more accurate uncertainty measures than the standard deviations. In the constant magnetic field intensity case, the energy varies linearly with the quantum numbers n and m and B0. As expected, no transitions takes place because the states describing the particle are stationary. In the oscillatory case, we observe that the energy oscillates in time, increasing linearly with the Landau levels n and m and nonlinearly with the magnetic field. The (k,l)→(n,m) transitions take place only for l=m. We also investigate the (0,0)→(n,0) and (1,l)→(2,l) probability transitions.m