Photon Packet Energy Budget Boundary Scan - Quantum Mechanics IV: Photons, Interferometers, and Optical Qubits Step by Step

The packet-energy scan checks how many photons fit inside a fixed energy budget. The toy photon energy stays fixed while the packet count changes, so one row lands on the budget and the three-photon row exceeds it. Real photonic budgets also depend on source calibration, spectral spread, loss, detector response, finite counts, and uncertainty.

Photon count drives packet energy across a fixed budget. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Photon packet energy is counted against a budget

The toy photon energy is fixed; only the packet count changes.

m=E_{\max}-E_{\text{packet}}

Three packet counts bracket the energy budget

The middle row uses the whole budget. The final row exceeds it.

\begin{array}{c|c|c|c}N&E_{\text{packet}}&m&\text{gate}\\1&6&6&\text{pass}\\2&12&0&\text{pass}\\3&18&-6&\text{fail}\\\end{array}

The three-photon packet is over budget

The helper computes the total energy first; the lesson gate only compares it with the budget.

m=-6\quad \text{fail}