Phononen

Phononen is the plural form used in German-language physics to refer to the quantized lattice vibrational excitations of a crystalline solid; in English-language literature the corresponding term is phonons. The concept describes collective motions of atoms in a periodic lattice that behave like particles with quantized energy.

In solid-state physics a phonon is a quantum of vibrational energy in a crystal lattice. It arises from quantizing the normal modes of vibration of the lattice within the harmonic approximation. Each mode k has energy hbar*omega(k) and crystal momentum hbar*k.

Phononen are classified as acoustic or optical depending on the atomic displacement pattern in the basis. The dispersion relation omega(k) is determined by the crystal structure; acoustic branches are linear at long wavelengths, while optical branches have finite frequency at k = 0.

Quantization arises from treating lattice vibrations as coupled harmonic oscillators; creation and annihilation operators a†_k, a_k add or remove a phonon in mode k. Phononen play a central role in thermal transport, specific heat, and electron–phonon coupling that influences electrical resistance and superconductivity.

Experimentally, phononen are observed via inelastic neutron scattering, Raman spectroscopy, and infrared absorption; ultrasound techniques can probe long-wavelength modes. In German texts the plural is phononen; in English, phonons are used for both singular and plural. Phononen thus reflect the same physical concept as phonons, viewed through the linguistic lens of German-language physics literature.