A generalized Schr¨odinger approximation,due to Ikhdair & Sever,of the semi-relativistic two-body problem with a rectangular barrier in(1+1) dimensions is compared with exact computations.Exact and approximat...A generalized Schr¨odinger approximation,due to Ikhdair & Sever,of the semi-relativistic two-body problem with a rectangular barrier in(1+1) dimensions is compared with exact computations.Exact and approximate transmission and reflection coefficients are obtained in terms of local wave numbers.The approximate transmission and reflection coefficients turn out to be surprisingly accurate in an energy range |∈-V0| < 2μc^2,where μ is the reduced mass,∈ the scattering energy,and V_0 the barrier top energy.The approximate wave numbers are less accurate.展开更多
By applying an appropriate Pekeris approximation to deal with the centrifugal term, we present an approximate systematic solution of the two-body spinless Salpeter （SS） equation with the Woods-Saxon interaction pote...By applying an appropriate Pekeris approximation to deal with the centrifugal term, we present an approximate systematic solution of the two-body spinless Salpeter （SS） equation with the Woods-Saxon interaction potential for an arbitrary/-state. The analytical semi-relativistic bound-state energy eigenvalues and the corresponding wave functions are calculated. Two special cases from our solution are studied： the approximated SchrSdinger- Woods-Saxon problem for an arbitrary/-state and the exact s-wave （l=0）.展开更多
Scattering solutions of two-body Spinless Salpeter Equation(SSE) are investigated in the center of mass frame with a repulsive, symmetric Hulth′en potential in one spatial dimension. Transmission and reflection coeff...Scattering solutions of two-body Spinless Salpeter Equation(SSE) are investigated in the center of mass frame with a repulsive, symmetric Hulth′en potential in one spatial dimension. Transmission and reflection coefficients are calculated and discussed.展开更多
文摘A generalized Schr¨odinger approximation,due to Ikhdair & Sever,of the semi-relativistic two-body problem with a rectangular barrier in(1+1) dimensions is compared with exact computations.Exact and approximate transmission and reflection coefficients are obtained in terms of local wave numbers.The approximate transmission and reflection coefficients turn out to be surprisingly accurate in an energy range |∈-V0| < 2μc^2,where μ is the reduced mass,∈ the scattering energy,and V_0 the barrier top energy.The approximate wave numbers are less accurate.
文摘By applying an appropriate Pekeris approximation to deal with the centrifugal term, we present an approximate systematic solution of the two-body spinless Salpeter （SS） equation with the Woods-Saxon interaction potential for an arbitrary/-state. The analytical semi-relativistic bound-state energy eigenvalues and the corresponding wave functions are calculated. Two special cases from our solution are studied： the approximated SchrSdinger- Woods-Saxon problem for an arbitrary/-state and the exact s-wave （l=0）.
文摘Scattering solutions of two-body Spinless Salpeter Equation(SSE) are investigated in the center of mass frame with a repulsive, symmetric Hulth′en potential in one spatial dimension. Transmission and reflection coefficients are calculated and discussed.
