Geodesic
Stationary Schrödinger equations governing electronic states of quantum dots in the presence of spin-orbit splitting
Applications of Mathematics, Tome 52 (2007) no. 3, pp. 267-284.

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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 iterative projection method simultaneously handling the pair of nonlinear problems and thereby saving about 25 % of the computation time as compared to the Nonlinear Arnoldi method applied to each of the problems separately.
DOI : 10.1007/s10492-007-0014-5
Classification : 65F15, 65F50, 65H17, 81Q10
Keywords: quantum dot; nonlinear eigenvalue problem; minmax characterization; iterative projection method; electronic state; spin orbit interaction 
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     title = {Stationary {Schr\"odinger} equations governing electronic states of quantum dots in the presence of spin-orbit splitting},
     journal = {Applications of Mathematics},
     pages = {267--284},
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     volume = {52},
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Betcke, Marta M.; Voss, Heinrich. Stationary Schrödinger equations governing electronic states of quantum dots in the presence of spin-orbit splitting. Applications of Mathematics, Tome 52 (2007) no. 3, pp. 267-284. doi : 10.1007/s10492-007-0014-5. http://geodesic.mathdoc.fr/articles/10.1007/s10492-007-0014-5/

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