| |
| We analyze the relativistic bound states with mixed vector and scalar Woods-Saxon potentials, for particular under the specific coupling of V(r)=S(r) for s-wave states. As to spin-0 particles, the investigation via Klein-Gordon equation(KGE) indicates that besides the bound states and scattering states, an extra band gap with vanishing wave function arises. For the bound states, KGE is transformed into a hypergeometric equation with standard composition of the parameters, and on the analytic intervals of the extended argument R we obtain the solution via Gaussian series. The practical argument (0,1) and the Kummer solution at the regular singular point x=0, together with the boundary constraints, give rise to the s-wave discrete spectrum, analytically and explicitly. For the band gap, we prove its existence and investigate the properties. For this very energy interval, KGE differs slightly with that of the bound states after the same transformation, and could only be solved via series expansion, which shows that the wave function vanishes completely. This way, we obtain the structure of the bound state and band gap, the analytic wave function and the explicit energy spectrum for spin-0 particles. As to spin-1/2 particles, we apply Dirac equation(DE) based on the complete set [H,k,J2,J_z]. Under the specific coupling manner, the s-wave bound states lead to the identical radial DE with that of KGE, which yields the solution for the up component immediately, and subsequently induces the down component. These draw a clear picture of the behaviors of the spin-1/2 particles under such conditions. |
|
| Keywords:Relativistic Wave Equation;Woods-Saxon Potential;Bound State;Band Gap;Hypergeometric Equation |
|
