Two-State Populations

Equal Weights Make Equal Populations

Energy labels alone do not determine the shown population. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Equal explicit weights give equal populations

With equal weights, the upper fraction is one half.

Pupper=12P_{\rm upper}=\frac{1}{2}
Equal-weight contrastThe contrast changes weights, not hidden physics.energies=lower=0J|upper=2Jweights=lower=2|upper=2lowerFraction=1/2upperFraction=1/2upperLowerRatio=1weightOrigin=explicit integer weights

The population ratio is one

Equal weights make the upper-to-lower ratio one.

NupperNlower=1\frac{N_{\rm upper}}{N_{\rm lower}}=1
Equal population ratioThe ratio is recomputed exactly.energies=lower=0J|upper=2Jweights=lower=2|upper=2lowerFraction=1/2upperFraction=1/2upperLowerRatio=1weightOrigin=explicit integer weights