This paper is addressed to the problem of Galilei invariant basis construction for identical fermions systems. The recently introduced method for spurious state elimination from expansions in harmonic oscillator basis...This paper is addressed to the problem of Galilei invariant basis construction for identical fermions systems. The recently introduced method for spurious state elimination from expansions in harmonic oscillator basis [1] 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003400310034003400340037003600360038000000 is adopted and applied to bound states of two particles system with Coulomb potential description. Traditional expansions in this case demonstrate the extremely well-known slow convergence, and hence this is the best problem with known exact solutions for the test of the method. Obtained results demonstrate the significant simplification of the problem and fast convergence of expansions. We show that the application of this general method is very efficient in a test case of the energy spectrum calculation problem of two particles with different masses interacting with Coulomb potential.展开更多
A new method for calculation of non-relativistic energy spectrum of Coulomb three-body systems with two identical particles has been developed. The novelty of the method is the introduction of an expansion of the wave...A new method for calculation of non-relativistic energy spectrum of Coulomb three-body systems with two identical particles has been developed. The novelty of the method is the introduction of an expansion of the wave function on harmonic oscillator (HO) functions with different sizes in the Jacobi coordinates instead of only one unique size parameter in the traditional approach. The method presented obeys the principles of antisymmetry and translational invariance. The theoretical formulation has been illustrated by evaluation of ground state energies of a number of Coulomb three-body systems with two identical particles for zero HO excitation energy. The analytical solution of this problem in case of only one size parameter has been derived. The obtained results show significant advantage of the base with different sizes over the traditional approach for investigation of the bound state problem of quantum systems.展开更多
Single particles moving in a reflection-asymmetric potential are investigated by solving the Schr6dinger equation of the reflectionasymmetric Nilsson Hamiltonian with the imaginary time method in 3D lattice space and ...Single particles moving in a reflection-asymmetric potential are investigated by solving the Schr6dinger equation of the reflectionasymmetric Nilsson Hamiltonian with the imaginary time method in 3D lattice space and the harmonic oscillator basis expansion method. In the 3D lattice calculation, the l2 divergence problem is avoided by introducing a damping function, and the（l2）N term in the non-spherical case is calculated by introducing an equivalent N-independent operator. The efficiency of these numerical techniques is demonstrated by solving the spherical Nilsson Hamiltonian in 3D lattice space. The evolution of the single-particle levels in a reflection-asvmmetric ootential is obtained and discussed bv the above two numerical methods, and their consistencv is shown in the obtained single-particle energies with the differences smaller than 10-4[hω0]展开更多
文摘This paper is addressed to the problem of Galilei invariant basis construction for identical fermions systems. The recently introduced method for spurious state elimination from expansions in harmonic oscillator basis [1] 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003400310034003400340037003600360038000000 is adopted and applied to bound states of two particles system with Coulomb potential description. Traditional expansions in this case demonstrate the extremely well-known slow convergence, and hence this is the best problem with known exact solutions for the test of the method. Obtained results demonstrate the significant simplification of the problem and fast convergence of expansions. We show that the application of this general method is very efficient in a test case of the energy spectrum calculation problem of two particles with different masses interacting with Coulomb potential.
文摘A new method for calculation of non-relativistic energy spectrum of Coulomb three-body systems with two identical particles has been developed. The novelty of the method is the introduction of an expansion of the wave function on harmonic oscillator (HO) functions with different sizes in the Jacobi coordinates instead of only one unique size parameter in the traditional approach. The method presented obeys the principles of antisymmetry and translational invariance. The theoretical formulation has been illustrated by evaluation of ground state energies of a number of Coulomb three-body systems with two identical particles for zero HO excitation energy. The analytical solution of this problem in case of only one size parameter has been derived. The obtained results show significant advantage of the base with different sizes over the traditional approach for investigation of the bound state problem of quantum systems.
基金supported by the National Basic Research Program of China (Grant No. 2013CB834400)the National Natural Science Foundation of China (Grants Nos. 11335002, 11375015, 11461141002, and 11621131001)
文摘Single particles moving in a reflection-asymmetric potential are investigated by solving the Schr6dinger equation of the reflectionasymmetric Nilsson Hamiltonian with the imaginary time method in 3D lattice space and the harmonic oscillator basis expansion method. In the 3D lattice calculation, the l2 divergence problem is avoided by introducing a damping function, and the（l2）N term in the non-spherical case is calculated by introducing an equivalent N-independent operator. The efficiency of these numerical techniques is demonstrated by solving the spherical Nilsson Hamiltonian in 3D lattice space. The evolution of the single-particle levels in a reflection-asvmmetric ootential is obtained and discussed bv the above two numerical methods, and their consistencv is shown in the obtained single-particle energies with the differences smaller than 10-4[hω0]
