In weak measurement thought experiment, an ensemble consists of M quantum particles and N states. We observe that separability of the particles is lost, and hence we have fuzzy occupation numbers for the particles in the ensemble. Without sharply measuring each particle state, quantum interferences add extra possible configurations of the ensemble, this explains the Quantum Pigeonhole Principle. This principle adds more entropy to the system; hence the particles seem to have a new kind of correlations emergent from particles not having a single, well-defined state.

We have calculated the Zeeman-fine energies of atomic Lithium (Li) by using the varying effective Landé g-factor method. We take the principle quantum number in the range; (2 1 n 0  ). For this range we find 26 different energy values and 325 wavelengths some of which are the same. The Doppler shift is found to be  0.004      . The Doppler shift-corrected wavelengths are in perfect agreement with the observed (NIST) values for atomic Li.

We have calculated the effective Lande-g factors, g* for the entangled states in Hydrogen and Hydrogen-like atoms. We show that g* takes integer values such as 0,1,2,3,... .For (s − s) entanglement, we have g* = 0. For (s − p) entanglement, we have g* = 1 and so on. In general, for the entanglement of two states with angular momentum quantum numbers l1 and l2 we have g* =l1+l2.

We calculate the Zeeman-fine energies of atomic potassium by using the energy eigenvalues for hydrogen-like atoms for n < 11. We find 18 different energy values and 153 wavelengths some of which are the same. The calculated wavelengths are in good agreement with the observed values for potassium atom.