Stationary Schrödinger equations governing electronic states of quantum dots in the presence of spin-orbit splitting
Marta M. Betcke, Heinrich Voss (2007)
Applications of Mathematics
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In this work we derive a pair of nonlinear eigenvalue problems corresponding to the one-band effective Hamiltonian accounting for the spin-orbit interaction governing the electronic states of a quantum dot. We show that the pair of nonlinear problems allows for the minmax characterization of its eigenvalues under certain conditions which are satisfied for our example of a cylindrical quantum dot and the common InAs/GaAs heterojunction. Exploiting the minmax property we devise an efficient...