Energy level

An energy level is a discrete allowed energy value of a quantum system. Transitions between levels occur through interactions that exchange energy with the system.

Quantum state: A mathematical description of a quantum system that encodes its possible measurement outcomes. An energy level is a possible value of energy associated with a quantum state.
Planck constant: The fundamental constant setting the scale of quantum effects and relating energy to frequency. It converts transition frequencies into energy differences through the relation E = hν.
Hydrogen atom: The simplest atom, consisting of one proton and one electron bound by electromagnetic attraction. Its level energies have an exact, historically decisive solution in nonrelativistic quantum mechanics.
Atomic spectroscopy: The study of atoms through their emission, absorption, or scattering of electromagnetic radiation. Measured spectral transitions reveal differences between atomic energy levels.
Continuous spectrum: A range of spectral values without discrete gaps between allowed values. It contrasts with isolated energy levels in bound quantum systems.
Hamiltonian operator: The operator representing a quantum system’s total energy and generating its time evolution. Its eigenvalues are the system’s allowed energy levels.
Schrödinger equation: The equation governing how a nonrelativistic quantum state changes and which stationary states are allowed. Solving its stationary form yields allowed energy levels for many systems.
Particle in a box: An idealized quantum particle confined to a region with impenetrable boundaries. Its simple discrete levels demonstrate how confinement quantizes energy.
Laser: A device that generates coherent light through stimulated emission in an active medium. Lasers exploit transitions between selected energy levels to amplify light.
Energy band: A range of closely spaced allowed electron energies in a solid, formed from many interacting atoms. Many neighboring levels in a solid merge into bands rather than remaining isolated.

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