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In position representation,which differentiates only with respect to $x$ and $y$. Multiplication by $z$ therefore commutes with it:Taking the matrix element of this commutator between angular-momentum eigenstates givesThus the matrix element can be nonzero only whenThis is the magnetic part of the electric-dipole selection rules for hydrogen.

The even, spherically symmetric hydrogen ground state has no permanent electric dipole, so a uniform electric field gives no first-order energy shift. Odd-parity excited states mix in at second order, yielding a negative shift quadratic in the field.