Resonance Selects a Transition - Quantum Mechanics: Waves, Spin, and Tunneling Step by Step

Quantum control begins with matching a pulse to an energy gap in a finite model. 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 matched pulse selects the gap

The modeled energy gap is 3/4. A pulse with the same value is checked as matched.

\Delta E=\frac{3}{4}

Matched and mismatched rows compare pulse to gap

The same gap is tested against two exact pulse values, one matching and one not.

\begin{array}{c|c|c|c}\text{case}&\Delta E&\text{pulse}&\text{gate}\\\text{matched}&\frac{3}{4}&\frac{3}{4}&\text{pass}\\\text{missed}&\frac{3}{4}&\frac{1}{2}&\text{fail}\\\text{gap}&\frac{3}{4}&\frac{3}{4}&\text{source}\\\end{array}

A mismatched pulse gives no modeled transition

A contrast pulse of 1/2 does not match the same gap in this model.

\text{pulse}=\frac{1}{2}\neq \frac{3}{4}