Quantum wells, wires and dots with finite barrier: analytical expressions for the bound states

Details Quantum wells, wires and dots with finite barrier: analytical expressions for the bound states Quantum wells, wires and dots with finite barrier: analytical expressions for the bound states

2002-01-30

arxiv.org/abs/cond-mat/0201553v1

Solid State Communication 119 (2001) 631-635

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 3 figures

Scientific paper

From a careful study of the transcendental equations fulfilled by the bound state energies of a free particle in a quantum well, cylindrical wire or spherical dot with finite potential barrier, we have derived analytical expressions of these energies which reproduce impressively well the numerical solutions of the corresponding transcendental equations for all confinement sizes and potential barriers, without any adjustable parameter. These expressions depend on a unique dimensionless parameter which contains the barrier height and the sphere, wire or well radius.

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