Abstract
In this work we study the Dirac equation in a curved static space–time, where the metric depends on two arbitrary functions f(r) and g(r), namely the line element is ds2=e2f(r)dt2−e2g(r)dr2−r2dθ2−r2sin2θdϕ2. We exactly solve the angular equation for arbitrary f(r) and g(r). Then, we uncouple the radial component of the spinor for a metric model defined by f=g and find the exact solutions for three quantum systems: Hydrogen atom, Dirac–Morse oscillator and a linear radial potential by V(r)=ar.
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