Two-State Populations

Lower State Can Dominate the Population

A lower state can dominate when its explicit weight is larger. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Weights set the population fractions

The lower state has three shares and the upper state has one share.

Plower=34,Pupper=14P_{\rm lower}=\frac{3}{4},\quad P_{\rm upper}=\frac{1}{4}
Two-state populationFractions are computed from explicit weights.energies=lower=0J|upper=2Jweights=lower=3|upper=1lowerFraction=3/4upperFraction=1/4upperLowerRatio=1/3weightOrigin=explicit integer weights

The upper fraction is one quarter

The upper-state population is one quarter of the finite ledger.

Pupper=14P_{\rm upper}=\frac{1}{4}
Upper population fractionThe energy labels alone do not set the fraction.energies=lower=0J|upper=2Jweights=lower=3|upper=1lowerFraction=3/4upperFraction=1/4upperLowerRatio=1/3weightOrigin=explicit integer weights