We apply an approximation to the centrifugal term and solve the two-body spinless-Salpeter equation （SSE） with the Yukawa potential via the supersymmetric quantum mechanics （SUSYQM） for arbitrary quantum numbers. ...We apply an approximation to the centrifugal term and solve the two-body spinless-Salpeter equation （SSE） with the Yukawa potential via the supersymmetric quantum mechanics （SUSYQM） for arbitrary quantum numbers. Useful figures and tables are also included.展开更多
We study the eigenvalues of the rotating Morse potential by using the quantization condition from the analytical transfer matrix（ATM） method.A hierarchy of supersymmetric partner potentials is obtained with Pekeris ...We study the eigenvalues of the rotating Morse potential by using the quantization condition from the analytical transfer matrix（ATM） method.A hierarchy of supersymmetric partner potentials is obtained with Pekeris approximation,which can be used to calculate the energies of higher rotational states from the energies of lower states.The energies of rotational states of the hydrogen molecule are calculated by the ATM condition,and comparison of the results with those from the hypervirial perturbation method reveals that the accuracy of the approximate expression of Pekeris for the eigenvalues of the rotating Morse potential can be improved substantially in the framework of supersymmetric quantum mechanics.展开更多
This paper shows that one type of first order Dirac equation with vector coupling and scalar coupling potentials can be brought into the framework of non relativistic supersymmetric quantum mechanics. The conclusion...This paper shows that one type of first order Dirac equation with vector coupling and scalar coupling potentials can be brought into the framework of non relativistic supersymmetric quantum mechanics. The conclusion is independent of the concrete forms of the vector and scalar coupling potentials because of the nilpotent matrix realization of supersymmetric quantum mechanical algebra. The supersymmetry of this kind of Dirac equation requires that a spin orbit coupling term be introduced into the associated supersymmetric Hamiltonian.展开更多
There are two kinds of recurrence relations for the spherical functions Pml. The first are those with the same m but different l. Thesecond are those with the same l but different m. The spheroidal functions are exten...There are two kinds of recurrence relations for the spherical functions Pml. The first are those with the same m but different l. Thesecond are those with the same l but different m. The spheroidal functions are extensions of the spherical functions. Recurrencerelations of the first kind are obtained for the spheroidal functions in recent studies. Using the shape invariance method in super-symmetric quantum mechanics, we investigate the second type of recurrence relations for the spheroidal functions. The resultsshow that the second kind of recurrence relation can not be extended to the spheroidal functions.展开更多
The integrable properties of the spheroidal equations are investigated. The shape-invariance property is proved to be retained for the spheroidal equations, for which the recurrence relations are obtained. This is the...The integrable properties of the spheroidal equations are investigated. The shape-invariance property is proved to be retained for the spheroidal equations, for which the recurrence relations are obtained. This is the extension of the recurrence relation of the Legendre polynomials.展开更多
We investigate the approximate solution of the Dirac equation for a combination of Mobius square and Mie type potentials under the pseudospin symmetry limit by using supersymmetry quantum mechanics. We obtain the boun...We investigate the approximate solution of the Dirac equation for a combination of Mobius square and Mie type potentials under the pseudospin symmetry limit by using supersymmetry quantum mechanics. We obtain the bound-state energy equation and the corresponding spinor wave functions in an approximate analytical manner. We comment on the system via various useful figures and tables.展开更多
文摘We apply an approximation to the centrifugal term and solve the two-body spinless-Salpeter equation （SSE） with the Yukawa potential via the supersymmetric quantum mechanics （SUSYQM） for arbitrary quantum numbers. Useful figures and tables are also included.
基金Project supported by the Fund from the Science and Technology Committee of Shanghai Municipality,China (Grant No. 11ZR1412300)the National Natural Science Foundation of China (Grant No. 61108010)
文摘We study the eigenvalues of the rotating Morse potential by using the quantization condition from the analytical transfer matrix（ATM） method.A hierarchy of supersymmetric partner potentials is obtained with Pekeris approximation,which can be used to calculate the energies of higher rotational states from the energies of lower states.The energies of rotational states of the hydrogen molecule are calculated by the ATM condition,and comparison of the results with those from the hypervirial perturbation method reveals that the accuracy of the approximate expression of Pekeris for the eigenvalues of the rotating Morse potential can be improved substantially in the framework of supersymmetric quantum mechanics.
基金Tsinghua Basic Science Foundation!( 98JC0 79) partially by the National NaturalScience Foundation of China!( No.1990 5 0
文摘This paper shows that one type of first order Dirac equation with vector coupling and scalar coupling potentials can be brought into the framework of non relativistic supersymmetric quantum mechanics. The conclusion is independent of the concrete forms of the vector and scalar coupling potentials because of the nilpotent matrix realization of supersymmetric quantum mechanical algebra. The supersymmetry of this kind of Dirac equation requires that a spin orbit coupling term be introduced into the associated supersymmetric Hamiltonian.
基金supported by the National Natural Science Foundation of China (Grant No. 10875018)the National Basic Research Program of China (Grant No. 2010CB923200)
文摘There are two kinds of recurrence relations for the spherical functions Pml. The first are those with the same m but different l. Thesecond are those with the same l but different m. The spheroidal functions are extensions of the spherical functions. Recurrencerelations of the first kind are obtained for the spheroidal functions in recent studies. Using the shape invariance method in super-symmetric quantum mechanics, we investigate the second type of recurrence relations for the spheroidal functions. The resultsshow that the second kind of recurrence relation can not be extended to the spheroidal functions.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10875018 and 10773002)
文摘The integrable properties of the spheroidal equations are investigated. The shape-invariance property is proved to be retained for the spheroidal equations, for which the recurrence relations are obtained. This is the extension of the recurrence relation of the Legendre polynomials.
文摘We investigate the approximate solution of the Dirac equation for a combination of Mobius square and Mie type potentials under the pseudospin symmetry limit by using supersymmetry quantum mechanics. We obtain the bound-state energy equation and the corresponding spinor wave functions in an approximate analytical manner. We comment on the system via various useful figures and tables.
