Exact hole-bound states for semiconductor quantum wells with arbitrary potential profiles

V. I. Galiev*, E. M. Goldys, M. G. Novak, A. F. Polupanov, T. L. Tansley

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Citation (Scopus)


An efficient numerical-analytical method for finding confined and continuum states in quantum-well systems with arbitrary potential profiles, described by coupled Schrödinger equations, is presented. The method is based on the analytical properties of the wave functions, in particular, the power series representation of solutions of the corresponding coupled differential equations. Using only the general properties of the coefficients of a system of an arbitrary number of coupled Schrödinger equations, and imposing for definiteness the simplest boundary conditions, we derive exact expressions for the wave functions and present methods for accurate calculations of the energies and wave functions of confined states and of the wave functions of continuum states in quantum wells. The method is applied to the calculation of the dispersion of hole bound states in a single GaAs quantum well with truncated parabolic confining potentials of different strengths. The results are compared with data available from previous calculations.

Original languageEnglish
Pages (from-to)421
Number of pages1
JournalSuperlattices and Microstructures
Issue number4
Publication statusPublished - Jun 1995

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