Triangular quantum profiles: transmission probability and energy spectrum

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Arda A.

TURKISH JOURNAL OF PHYSICS, vol.41, no.1, pp.72-80, 2017 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 1
  • Publication Date: 2017
  • Doi Number: 10.3906/fiz-1607-8
  • Journal Name: TURKISH JOURNAL OF PHYSICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.72-80
  • Hacettepe University Affiliated: Yes

Abstract

Analytical expressions for the transition probability and the energy spectrum of the 1D Schrdinger equation with position-dependent mass are presented for the triangular quantum barrier and quantum well. The transmission coefficient is obtained by using the wave functions written in terms of Airy's functions and of the solutions of Kummer's differential equation. In order to show the validity of our analysis, an example by taking some numerical values for a GaAs heterostructure is presented.