We have constructed a set of non-Hermitian operators that satisfy the commutation relations of the SO(3)-Lie algebra. Using these set of operators we have constructed a non-Hermitian Hamiltonian corresponding to the Hydrogen atom that includes a complex term but with the same spectra as in the Hermitian case. It is also found a non-Hermitian Runge–Lenz vector that represents a conserved quantity. In this way, we obtain a set of non-Hermitian operators that satisfy the commutation relations of the SO(4)-Lie algebra.
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