Phonon Fit Window Three-Row Scan - Solid-State Physics: Lattices, Phonons, and Band Filling Step by Step

Wavelength moves below, onto, and above a standing-mode fit. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Short wavelength misses the standing window

Mode index stays fixed while wavelength moves through the exact fit window. The fit bit is checked by the rendered mode source.

\begin{array}{c}n\lambda=3\cdot 6=18\ \mathrm{m}\ \ne\ 24\ \mathrm{m}\\fit=0,\quad nodes=4\end{array}

Matching wavelength fits the standing window

Mode index stays fixed while wavelength moves through the exact fit window. The fit bit is checked by the rendered mode source.

\begin{array}{c}n\lambda=3\cdot 8=24\ \mathrm{m}\ =\ 24\ \mathrm{m}\\fit=1,\quad nodes=4\end{array}

Long wavelength overshoots the standing window

Mode index stays fixed while wavelength moves through the exact fit window. The fit bit is checked by the rendered mode source.

\begin{array}{c}n\lambda=3\cdot 10=30\ \mathrm{m}\ \ne\ 24\ \mathrm{m}\\fit=0,\quad nodes=4\end{array}