grundtilstanden

Grundtilstanden, commonly translated as the ground state, is the lowest energy state of a quantum system described by its Hamiltonian. It corresponds to the smallest energy eigenvalue E0 and to the associated eigenfunction or wavefunction, which serves as the reference point for all higher-energy, or excited, states. For stationary systems, the ground state has a fixed probability distribution and a time evolution that is only a global phase, making its observable properties time-independent.

Key properties include its role as the system’s most stable configuration. In simple systems, such as the quantum harmonic oscillator, the ground state possesses nonzero zero-point energy (for example, E0 = ħω/2) and intrinsic quantum fluctuations in observables like position and momentum. The ground state's degeneracy depends on symmetries of the Hamiltonian; it can be unique or multiple if the system has symmetry-induced degeneracy.

In many-body physics and chemistry, the ground state determines fundamental properties such as bonding, electronic structure, and phase behavior. At zero temperature, a system is presumed to occupy its ground state; at finite temperatures, excited states are thermally populated according to Boltzmann statistics. The energy gap to the first excited state influences whether a material behaves as an insulator or a metal, among other phenomena.

Origins and usage: the term Grundtilstanden is the Scandinavian variant of the German Grundzustand, used widely in physics and chemistry to denote the lowest-energy configuration of a system.