| Within the effective-mass approximation we calculate the energies of a donor impurityand single electron in an elliptical quantum ring subjected to a magnetic field using themethod of exact numerical diagonalization in this paper. The result shows that due to theAharonov–Bohm effect in the presence of the ring, the energies of the single electron and thedonor impurity are found to exhibit oscillations depending on the magnetic field, thisoscillation is called AB oscillation. In the single electron system, as the eccentricity of thequantum ring increases, ring becomes flatter and flatter, geometrical confinement becomesstronger, the energies and period gradually increase. In the donor impurity system, theelectron is also subjected to Coulomb potential. When the magnetic field is weak, as theeccentricity increases, the ground state energy gradually decreases, the Coulomb potentialplays a dominant role. When the magnetic field is strong, as the eccentricity increases, theground state energy gradually becomes stronger, geometrical confinement and magnetic fieldplay a dominant role. As the ring becomes flatter and flatter, the wave functions are notwell-distributed, the period of the AB oscillation increases.In this paper, we also calculate the energies of single electron in an elliptical quantumplate with special function method and exact numerical diagonalization method. The resultsare discussed in detail and both methods are compared. The conclusions of both methods areidentical. The energies are described by two quantum numbers: order mand radial wavenode n. m and nequal all possible value, there are infinite energies, these energiescompose the system energy level. Onlym=0and n=0, the system energy is the groundstate energy. As the eccentricity of the elliptical quantum plate increases, plate becomesflatter and flatter, geometrical confinement becomes stronger, the energies gradually increase. |
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