TY - JOUR
T1 - Quantum features of semiconductor quantum dots
AU - Lozada-Cassou, M.
AU - Dong, Shi Hai
AU - Yu, Jiang
N1 - Funding Information:
One of the authors (S.H. Dong) would like to thank Prof. Zhong-Qi Ma for the helpful discussions and invaluable suggestions. Also, the authors would like to thank the referee for the positive and invaluable suggestions from which the manuscript is improved greatly. This work was partially supported by IMP, Mexico.
PY - 2004/10/11
Y1 - 2004/10/11
N2 - The exact solutions of the two-dimensional Schrödinger equation with the position-dependent mass for the square well potential in the semiconductor quantum dots system are obtained. The eigenvalues, which are closely related to the position-dependent masses μ1 and μ2, the potential well depth V0 and the radius of the quantum dots r 0, can be calculated from two boundary conditions. We generalize this quantum system to three-dimensional case. The special cases for the angular momentum quantum number l=0, 1, 2 are studied in some detail. We find that the energy levels are proportional to the parameters μ2, V0 and r0 for l=0. The relations between them for l=1, 2 become very complicated. The scattering states of this quantum system are mentioned briefly.
AB - The exact solutions of the two-dimensional Schrödinger equation with the position-dependent mass for the square well potential in the semiconductor quantum dots system are obtained. The eigenvalues, which are closely related to the position-dependent masses μ1 and μ2, the potential well depth V0 and the radius of the quantum dots r 0, can be calculated from two boundary conditions. We generalize this quantum system to three-dimensional case. The special cases for the angular momentum quantum number l=0, 1, 2 are studied in some detail. We find that the energy levels are proportional to the parameters μ2, V0 and r0 for l=0. The relations between them for l=1, 2 become very complicated. The scattering states of this quantum system are mentioned briefly.
KW - Exact solutions
KW - Position-dependent mass
KW - Quantum dots
UR - http://www.scopus.com/inward/record.url?scp=4644278448&partnerID=8YFLogxK
U2 - 10.1016/j.physleta.2004.08.047
DO - 10.1016/j.physleta.2004.08.047
M3 - Artículo
SN - 0375-9601
VL - 331
SP - 45
EP - 52
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 1-2
ER -