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An Exactly Solvable Algebraic Model for Single Quantum Well Treatments

DOI: 10.4236/am.2013.410A3002    3,199 Downloads   4,910 Views  

ABSTRACT

We propose an algebraic model, presenting individual contributions separately in the system of interest, for the exact solutions of one-dimensional Poisson-Schr?dinger equations used generally in semiconductor device simulations. The model presented here reveals an interesting relation between the corresponding Poisson and Schr?dinger equation for the physical structure considered, which leads to closed solutions without solving the required electrostatic equation.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

B. Gönül, Ö. Ünsal and B. Gönül, "An Exactly Solvable Algebraic Model for Single Quantum Well Treatments," Applied Mathematics, Vol. 4 No. 10C, 2013, pp. 7-13. doi: 10.4236/am.2013.410A3002.

References

[1] M. T. Edmonds, C. I. Pakes and L. Ley, “Self-Consistent Solution of the Schrodinger-Poisson Equations for Hy drogen-Terminated Diamond,” Physical Review B, Vol. 81, No. 8, 2010, Article ID: 85314. http://dx.doi.org/10.1103/PhysRevB.81.085314
[2] B. Sutherland, “Beautiful Models,” World Scientific, Singapore, 2004.
[3] O. Ciftja, “A Jastrow Correlation Factor for Two-Di mensional Parabolic Quantum Dots,” Modern Physics Letters B, Vol. No. 26, 2009, p. 3055. http://dx.doi.org/10.1142/S0217984909021120
[4] G. Levai and O. Ozer, “An Exactly Solvable Schrodinger Equation with Finite Positive Position-Dependent Effec tive Mass,” Journal of Mathematical Physics, Vol. 51, 2010, Article ID: 92103. http://dx.doi.org/10.1063/1.3483716
[5] A. R. Plastino, A. Puente, M. Casas, F. Garcias and A. Plastino, “Bound States in Quantum Systems with Posi tion Dependent Effective Masses,” Revista Mexicana de Física, Vol. 46, No. 1, 2000, pp. 78-84.
[6] G. Gonzalez, “Relation between Poisson and Schrodinger Equations” American Journal of Physics, Vol. 80, No. 8, 2012, pp. 715-719.
[7] P. Harrison, “Quantum Wells, Wires and Dotes,” John Wiley, Hoboken, 2000.
[8] G. D. Mahan, “Quantum Mechanics in a Nutshell,” Prin ceton University, Princeton, 2009.

  
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