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In order to go from a quantum system to a classical one, all orientations need to become available again, so that the energy varies continuously. The sign can be fixed by choosing V_zz and Q appropriately. The problem that still remains is the ratio of the energies. The classical system has that the increase for m=+-1 is twice that of the decrease of m=0, while this is opposite for the quantum system. If we could change this for the quantum system it would reduce well to the classical system.
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