CND-05

Phonon oscillator energy

U = ħω / (e^{ħω/kT} − 1). Mean energy of one Bose mode (zero-point omitted).

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PhononsPhonon

Governing equation

U=\dfrac{\hbar\omega}{e^{\hbar\omega/kT}-1}

where

f: Frequency (THz)
T: Temperature (K)
U: Mode energy (meV)

Lecture brief

Historical brief

Drude electrons, Bloch waves, BCS pairing (1957) and Wiedemann–Franz heat are the first solids-and-metals laws. The lab is conductivity, gap and phonon heat in closed form. This sheet (CND-05 — Phonon oscillator energy) is the form associated with Phonon. Working symbols: $f$ , $T$ $\rightarrow$ $U$ . The heat capacity of a solid is the T-derivative of a sum of such modes.

Purpose

Purpose: compute

U

from

f

T

in Condensed matter via

U=\dfrac{\hbar\omega}{e^{\hbar\omega/kT}-1}

U = ħω / (e^{ħω/kT} − 1). Mean energy of one Bose mode (zero-point omitted). Use it when a real condensed matter question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

f = 5.000\,\mathrm{THz}

T = 300.000\,\mathrm{K}

, the governing relation

U=\dfrac{\hbar\omega}{e^{\hbar\omega/kT}-1}

yields

U = 16.877\,\mathrm{meV}

. A lattice spring, a Bose occupation. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Frequency f5 THzTemperature T300 K

Outputs

Mode energy U16.877 meV

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Narration of this film

A lattice spring, a Bose occupation.

The heat capacity of a solid is the T-derivative of a sum of such modes.

Reading speed

Watch on YouTube