Energiniveau

Energiniveau is the Dutch term for energy level and refers to the discrete energy value a quantum system may possess. In quantum mechanics, particles are described by wavefunctions, and solutions to the time-independent Schrödinger equation yield a set of energy eigenvalues. Each eigenvalue corresponds to an energetic state, and states sharing the same eigenvalue are degenerate. Levels are typically labeled by quantum numbers appropriate to the system (for atoms: principal n, angular momentum l, magnetic m; for molecules: electronic, vibrational, and rotational indices).

Transitions between levels involve absorption or emission of energy equal to the difference between levels, ΔE = hν. At finite temperature, populations of levels follow statistical distributions, such as the Boltzmann distribution, subject to the Pauli exclusion principle for fermions. Spectroscopy probes energy levels by measuring photons absorbed or emitted when transitions occur; selection rules constrain which transitions are allowed (for atomic electrons, Δl ≈ ±1; for vibrational transitions, Δv ≈ ±1 in the harmonic approximation; rotational transitions follow ΔJ = ±1).

Examples: In hydrogen-like atoms, energy levels follow En = -R∞/n^2. In molecules, energy levels form electronic, vibrational, and rotational ladders, producing characteristic spectra. In solids, discrete levels broaden into energy bands due to the periodic lattice potential; band structure determines electrical and optical properties.

Measurement methods include absorption and emission spectroscopy, photoelectron spectroscopy, and tunneling spectroscopy. Understanding energy levels underpins fields from fundamental physics to chemistry and materials science, and practical devices such as lasers rely on controlled transitions between levels.