We use a recently defined quantum spectral function and apply the method of closed-orbit theory to the 2D circular billiard system. The quantum spectra contain rich information of all classical orbits connecting two a...We use a recently defined quantum spectral function and apply the method of closed-orbit theory to the 2D circular billiard system. The quantum spectra contain rich information of all classical orbits connecting two arbitrary points in the well. We study the correspondence between quantum spectra and classical orbits in the circular, 1/2 circular and 1/4 circular wells using the analytic and numerical methods. We find that the peak positions in the Fourier- transformed quantum spectra match accurately with the lengths of the classical orbits. These examples show evidently that semi-classlcal method provides a bridge between quantum and classical mechanics.展开更多
We calculate the photodetachment cross sections of H- in a gradient electric field based on traditional quantum approach. The system provides a rare example that the formulas for the cross sections can be explicitly d...We calculate the photodetachment cross sections of H- in a gradient electric field based on traditional quantum approach. The system provides a rare example that the formulas for the cross sections can be explicitly derived by both the quantum approach and closed-orbit theory. The quantum results are compared with those of the closed-orbit theory. The correct phase values in the closed-orbit theory are essential and necessary to produce accurate cross sections. Our quantum results remove some previous ambiguities in assigning the phase values in the closed-orbit theory （G. C. Yang and M. L. Du 2007 Phys. Rev. A 75 029904E）.展开更多
We report a theoretical scheme using a B-spline basis set to improve the poor computational accuracy ofcircular Rydberg states of hydrogen atoms in the intermediate magnetic Geld.This scheme can produce high accuracye...We report a theoretical scheme using a B-spline basis set to improve the poor computational accuracy ofcircular Rydberg states of hydrogen atoms in the intermediate magnetic Geld.This scheme can produce high accuracyenergy levels and valid for an arbitrary magnetic field.Energy levels of hydrogen are presented for circular Rydbergstates with azimuthal quantum numbers \m\ = 10-70 as a function of magnetic field strengths ranging from zero to2.35 x 109 T.The variation of spatial distributions of electron probability densities with magnetic field strengths isdiscussed and competition between Coulomb and magnetic interactions is illustrated.展开更多
The photodetachment cross section of H- in a linear harmonic oscillator potential is investigated. This system pro- vides a rare example that can be studied analytically by both quantum and semiclassical methods with ...The photodetachment cross section of H- in a linear harmonic oscillator potential is investigated. This system pro- vides a rare example that can be studied analytically by both quantum and semiclassical methods with some approxi- mations. The formulas of the cross section for different laser polarization directions are explicitly derived by both the traditional quantum approach and closed-orbit theory. In the traditional quantum approach, we calculate the cross sections in coordinate representation and momentum representation, and get the same formulas. We compare the quantum formulas with closed-orbit theory formulas, and find that when the detachment electron energy is larger than hco, where co is the frequency of the oscillator potential, the quantum results are shown to be in good agreement with the semiclassical results.展开更多
Photodeachment of H^-near a reflective spherical surface was studied by Haneef et al.[J.Phys.B:At.Mol.Opt.Phys.44(2011)195004]using a theoretical imaging method.The total cross section displays interesting oscillation...Photodeachment of H^-near a reflective spherical surface was studied by Haneef et al.[J.Phys.B:At.Mol.Opt.Phys.44(2011)195004]using a theoretical imaging method.The total cross section displays interesting oscillations.Here we re-examine the total photodetachment cross section of this system by directly applying the standard closed-orbit theory.Our result for the total cross section differs from the result obtained by Haneef et al.The difference between the two results vanishes in the limit of large radius of the reflective sphere.We argue that the theoretical imaging method developed originally for photodetachment near a Hat surface can not be directly applied to the present system.展开更多
A recently developed B-spline algorithm is extended and utilized to calculate excited states of He atoms in the presence of strong magnetic fields.Binding energies are presented for He in the five excited atomic state...A recently developed B-spline algorithm is extended and utilized to calculate excited states of He atoms in the presence of strong magnetic fields.Binding energies are presented for He in the five excited atomic states 210-+,110-,210-,11(-1)+,and 2 1(1) + with magnetic field strength ranging from 0.0001 to 10 a.u.The obtained energies are compared with available theoretical data,and found to be in good agreement.We investigate influence of magnetic fields on atomic structures of multielectron atoms,and illustrate that how electron probability density distributions change with increasing magnetic field strength.The current approach is directly applicable to simulations of discrete spectra for He atoms in the atmospheres of magnetized white dwarf stars.展开更多
文摘We use a recently defined quantum spectral function and apply the method of closed-orbit theory to the 2D circular billiard system. The quantum spectra contain rich information of all classical orbits connecting two arbitrary points in the well. We study the correspondence between quantum spectra and classical orbits in the circular, 1/2 circular and 1/4 circular wells using the analytic and numerical methods. We find that the peak positions in the Fourier- transformed quantum spectra match accurately with the lengths of the classical orbits. These examples show evidently that semi-classlcal method provides a bridge between quantum and classical mechanics.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10804066 and 11074260)the Natural Science Foundation of Shanxi Province of China (Grant No. 2009011004)
文摘We calculate the photodetachment cross sections of H- in a gradient electric field based on traditional quantum approach. The system provides a rare example that the formulas for the cross sections can be explicitly derived by both the quantum approach and closed-orbit theory. The quantum results are compared with those of the closed-orbit theory. The correct phase values in the closed-orbit theory are essential and necessary to produce accurate cross sections. Our quantum results remove some previous ambiguities in assigning the phase values in the closed-orbit theory （G. C. Yang and M. L. Du 2007 Phys. Rev. A 75 029904E）.
基金Support from National Science Foundation of USA under Grant No. 0630370National Natural Science Foundation of China under Grant Nos. 90403028 and 11074260
文摘We report a theoretical scheme using a B-spline basis set to improve the poor computational accuracy ofcircular Rydberg states of hydrogen atoms in the intermediate magnetic Geld.This scheme can produce high accuracyenergy levels and valid for an arbitrary magnetic field.Energy levels of hydrogen are presented for circular Rydbergstates with azimuthal quantum numbers \m\ = 10-70 as a function of magnetic field strengths ranging from zero to2.35 x 109 T.The variation of spatial distributions of electron probability densities with magnetic field strengths isdiscussed and competition between Coulomb and magnetic interactions is illustrated.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11421063 and 11474079)the Natural Science Foundation of Shanxi Province,China(Grant No.2009011004)the Program for the Top Young Academic Leaders of Higher Learning Institutions of Shanxi Province,China
文摘The photodetachment cross section of H- in a linear harmonic oscillator potential is investigated. This system pro- vides a rare example that can be studied analytically by both quantum and semiclassical methods with some approxi- mations. The formulas of the cross section for different laser polarization directions are explicitly derived by both the traditional quantum approach and closed-orbit theory. In the traditional quantum approach, we calculate the cross sections in coordinate representation and momentum representation, and get the same formulas. We compare the quantum formulas with closed-orbit theory formulas, and find that when the detachment electron energy is larger than hco, where co is the frequency of the oscillator potential, the quantum results are shown to be in good agreement with the semiclassical results.
基金Supported by National Natural Science Foundation of China under Grant Nos.11474079 and 11421063
文摘Photodeachment of H^-near a reflective spherical surface was studied by Haneef et al.[J.Phys.B:At.Mol.Opt.Phys.44(2011)195004]using a theoretical imaging method.The total cross section displays interesting oscillations.Here we re-examine the total photodetachment cross section of this system by directly applying the standard closed-orbit theory.Our result for the total cross section differs from the result obtained by Haneef et al.The difference between the two results vanishes in the limit of large radius of the reflective sphere.We argue that the theoretical imaging method developed originally for photodetachment near a Hat surface can not be directly applied to the present system.
基金Supported by the National Science Foundation of USA under Grant No. 0630370National Natural Science Foundation of Chinaunder Grant Nos. 90403028 and 11074260
文摘A recently developed B-spline algorithm is extended and utilized to calculate excited states of He atoms in the presence of strong magnetic fields.Binding energies are presented for He in the five excited atomic states 210-+,110-,210-,11(-1)+,and 2 1(1) + with magnetic field strength ranging from 0.0001 to 10 a.u.The obtained energies are compared with available theoretical data,and found to be in good agreement.We investigate influence of magnetic fields on atomic structures of multielectron atoms,and illustrate that how electron probability density distributions change with increasing magnetic field strength.The current approach is directly applicable to simulations of discrete spectra for He atoms in the atmospheres of magnetized white dwarf stars.
