A powerful approach to solve the Coulombic quantum three-body problem is proposed. The approach is exponentially convergent and more efficient than the hyperspherical coordinate method and the correlation-function hyp...A powerful approach to solve the Coulombic quantum three-body problem is proposed. The approach is exponentially convergent and more efficient than the hyperspherical coordinate method and the correlation-function hyperspherical harmonic method. This approach is numerically competitive with the variational methods, such as that using the Hylleraas-type basis functions. Numerical comparisons are made to demonstrate the efficiency of this approach, by calculating the nonrelativistic and infinite-nuclear-mass limit of the ground state energy of the helium atom. The exponential convergency of this approach is due to the full matching between the analytical structure of the basis functions that are used in this paper and the true wavefunction. This full matching was not reached by most other methods. For example, the variational method using the Hylleraas-type basis does not reflects the logarithmic singularity of the true wavefunction at the origin as predicted by Bartlett and Fock. Two important approaches are proposed in this work to reach this full matching: the coordinate transformation method and the asymptotic series method. Besides these, this work makes use of the least square method to substitute complicated numerical integrations in solving the Schr?dinger equation without much loss of accuracy, which is routinely used by people to fit a theoretical curve with discrete experimental data, but here is used to simplify the computation.展开更多
The features of the low-lying spectra of four-body A<SUP>+</SUP>B<SUP>-</SUP>A<SUP>+</SUP>B<SUP>-</SUP> systems have been deduced based on symmetry. Using the method of ...The features of the low-lying spectra of four-body A<SUP>+</SUP>B<SUP>-</SUP>A<SUP>+</SUP>B<SUP>-</SUP> systems have been deduced based on symmetry. Using the method of few-body physics, we calculate the energy spectra of A<SUP>+</SUP>B<SUP>-</SUP>A<SUP>+</SUP>B<SUP>-</SUP> systems in a harmonic quantum dot. We find that the biexciton in a two-dimensional quantum dot may have other bound excited states and the quantum mechanical symmetry plays a crucial role in determining the energy levels and structures of the low-lying states.展开更多
文摘A powerful approach to solve the Coulombic quantum three-body problem is proposed. The approach is exponentially convergent and more efficient than the hyperspherical coordinate method and the correlation-function hyperspherical harmonic method. This approach is numerically competitive with the variational methods, such as that using the Hylleraas-type basis functions. Numerical comparisons are made to demonstrate the efficiency of this approach, by calculating the nonrelativistic and infinite-nuclear-mass limit of the ground state energy of the helium atom. The exponential convergency of this approach is due to the full matching between the analytical structure of the basis functions that are used in this paper and the true wavefunction. This full matching was not reached by most other methods. For example, the variational method using the Hylleraas-type basis does not reflects the logarithmic singularity of the true wavefunction at the origin as predicted by Bartlett and Fock. Two important approaches are proposed in this work to reach this full matching: the coordinate transformation method and the asymptotic series method. Besides these, this work makes use of the least square method to substitute complicated numerical integrations in solving the Schr?dinger equation without much loss of accuracy, which is routinely used by people to fit a theoretical curve with discrete experimental data, but here is used to simplify the computation.
文摘The features of the low-lying spectra of four-body A<SUP>+</SUP>B<SUP>-</SUP>A<SUP>+</SUP>B<SUP>-</SUP> systems have been deduced based on symmetry. Using the method of few-body physics, we calculate the energy spectra of A<SUP>+</SUP>B<SUP>-</SUP>A<SUP>+</SUP>B<SUP>-</SUP> systems in a harmonic quantum dot. We find that the biexciton in a two-dimensional quantum dot may have other bound excited states and the quantum mechanical symmetry plays a crucial role in determining the energy levels and structures of the low-lying states.
