Which potentials are spherically symmetric

The solution of the physical problems is always facilitated by the presence of symmetries. Spherical symmetry, allows the reduction of the stationary Dirac 

To one who is familiar with nonrelativistic quantum mechanic it may appear quite clear what is meant by a spherically symmetric potential— any potential that actually only depends on x, so that it is invariant under any rotation applied to the system. It is indeed true that a scalar function p satisfies (x) == 4 R ) for all rotation matrices R, if and only if it is a function of r = [x]. But a general potential in quantum mechanics is given by a Hermitian matrix, and the unitary operators (86) representing the rotations in the Hilbert space of the Dirac equation can also affect the spinor-components. Hence it is not quite straightforward to tell, which potentials are spherically symmetric. 

Since the free Dirac operator Ho commutes with the total angular momentum 

Obviously, the Dirac equation is invariant under rotations, whenever 

Both the 4 X 4 unit matrix I4 and the Dirac matrix (3 commute with the matrix exp(—i(/ n S), and therefore 

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