Joint State Table - Quantum Mechanics: Waves, Spin, and Tunneling Step by Step

Two quantum particles can be described by one joint amplitude table. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A pair has one joint amplitude table

The nonzero joint amplitudes sit on the zero-zero and one-one same-outcome cells. Each has probability 1/2.

P_{\text{same cells}}=\frac{1}{2}

Only the same-outcome cells are populated

The joint table is read cell by cell before any single correlation sentence is made.

\begin{array}{c|c|c}\text{cell}&P&\text{role}\\\text{zero-zero}&\frac{1}{2}&\text{same}\\\text{zero-one}&0&\text{mixed}\\\text{one-one}&\frac{1}{2}&\text{same}\\\end{array}

The mixed cells have zero probability

The zero-one and one-zero mixed cells have probability 0 in this basis.

P_{\text{mixed cells}}=0