Variational approach to quasi-two-dimensional hydrogenic impurities in arbitrary magnetic fields

Abstract

Highly excited energy levels of a hydrogenic impurity atom confined in a quantum well are calculated variationally as functions of magnetic fields applied in the direction of growth. The trial wave functions are constructed on the basis of parity and nodal surface conservation, and behave correctly in both the low-field and high-field limits. With only two variational parameters for each state, all the levels associated with different subbands can, in principle, be obtained for the whole range of magnetic-field strengths. Transition energies for 1s-np (n=2,3,4) transitions in GaAs/${\mathrm{Ga}}_{0.7}$${\mathrm{Al}}_{0.3}$As quantum wells are compared with far-infrared photoconductivity spectra up to 9 T with a well width of 125 \AA{}. Good agreement is found in every case.