Energietoestanden

Energietoestanden is the Dutch term for energy states, the discrete energy levels that a quantum system can occupy. In quantum mechanics are these the eigenstates of the system's Hamiltonian, with eigenvalues that are the allowed energy levels. The set of energietoestanden forms a basis for the system's Hilbert space, and any physical state can be expressed as a superposition of them.

In stationary states, the probability distribution is constant in time apart from a phase factor, so measurements of energy yield one of the eigenvalues with probabilities given by the state's expansion coefficients. Time evolution in the Schrödinger picture multiplies each energy component by exp(-i E_n t / ħ). Transitions between energietoestanden can occur when the system is perturbed, for example by electromagnetic fields, with allowed transitions governed by selection rules.

The ground state is the lowest energy state; higher energies are excited states. At finite temperature, populations of energietoestanden follow the Boltzmann distribution, so higher levels become more populated as temperature rises.

Examples include atoms, where electrons occupy discrete atomic levels and transitions produce spectral lines with energy differences ΔE = E_f - E_i, corresponding to photon energy hν. In solids, the concept extends to energy bands and gaps arising from periodic potentials, where electrons occupy states within bands rather than discrete levels.

Energietoestanden are central to fields such as spectroscopy, quantum chemistry, and solid-state physics, as they determine spectra, reaction dynamics, and electronic properties. Related concepts include energy eigenstates, the Hamiltonian, and spectral decomposition.