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The E2 algebra has three elements, J, u, and v, which satisfy the commutation relations [u,J]=iv, [v,J]=−iu, [u,v]=0. We can construct the Hamiltonian H=J2+gu, where g is a real parameter, from these elements. This Hamiltonian is Hermitian and consequently it has real eigenvalues. However, we can also construct the -symmetric and non-Hermitian Hamiltonian H=J2+igu, where...
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