Energiniveauet

Energiniveauet refers to the discrete energy states that a physical system can occupy. In quantum mechanics, bound systems are described by a set of energy eigenvalues of the system’s Hamiltonian, and particles such as electrons fill these levels according to quantum rules. An energiniveau diagram illustrates the allowed energies and the possible transitions between them.

The energy levels arise from solving the quantum mechanical problem for a given potential. Each level E_n may possess degeneracy g_n, and the occupation of these levels is governed by principles such as the Pauli exclusion principle. In atoms, energy levels are quantized and spacing depends on the effective nuclear charge and electron interactions. For hydrogen-like atoms, the energies scale approximately as E_n ∝ -1/n^2, while many-electron atoms produce more complex spectra due to electron repulsion and spin-orbit effects.

In solids, discrete levels broaden into bands due to the interaction of many atoms in a lattice. The valence band and conduction band describe occupied and available states, separated by a band gap. The Fermi level indicates the chemical potential at finite temperature and determines which states are thermally accessible.

Transitions between energy levels are associated with absorption or emission of photons, with energy ΔE = hν. Such transitions give rise to spectral lines and form the basis of techniques like spectroscopy and laser operation. Populations of levels at a given temperature are described by Boltzmann or Fermi–Dirac statistics, influencing the intensity of transitions.

Applications of the concept include atomic and molecular spectroscopy, semiconductor physics, lasers, photovoltaics, and quantum technologies. Real systems may exhibit broadened or shifted levels due to interactions with fields, lattice vibrations, or environmental coupling.