N-维无限深球势阱中Klein-Gordon方程和Dirac方程的解

精确求解了N-维无限深球势阱中的Klein-Gordon方程和Dirac方程,结果表明:在N-维无限深球势阱中,Klein-Gordon方程和Dirac方程的径向方程在形式上与非相对论中的三维中心场的径向方程一致,均为贝塞尔方程。通过求解Bessel方程,任意束缚态的本征函数已被获得,其解可用通常的球贝塞尔函数表示。利用径向波函数在r=a处的连续性条件,其相应的能谱公式也被发现.对于Klein-Gordon方程:En2r,l′=m2 xn2r,l′/a2,而对于Dirac方程,则En2r,l′=-m2 m2a2 xn2,l′/a2.

Exact solutions to the Klein-Gordon and Dirac equations of the spherical potential well of infinite depth in N-space dimensions

The Klein-Gordon equation and Dirac equation of spherical potential well of infinite depth have been solved exactly in N-dimensions spaces.The results show that for spherical potential well of infinite depth,the radial equations of Klein-Gordon equation and Dirac equation are similar to the radial equation of three-dimensional schrdinger equation with spherical potential well of infinite depth.Through solving the Bessel equation,the radial wave function that can be expressed by the usual Bessel spherical function has been obtained for all bound states.The corresponding energy spectrum formulas (namely,E2nr,l'=m2+x2nr,l'/a2 and E2nr,l'=-m2+(√m2a2+x2nr,l'/a2)) also has been found by making use of the continuity of the radial wave function at r=a.