Energy level

A quantum mechanical system or particle that is bound, confined spatially, can only take on certain discrete values of energy, as opposed to classical particles, which can have any energy. These values are called energy levels. The term is most commonly used for the energy levels of electrons in atoms or molecules, which are bound by the electric field of the nucleus. The energy spectrum of a system with energy levels is said to be quantized.

If the potential energy is set to zero at infinity, the usual convention, then bound electron states have negative potential energy.

Energy levels are said to be degenerate, if the same energy level is shared by more than one quantum mechanical state. They are then called degenerate energy levels.

Quantized energy levels result from the relation between a particle's energy and its wavelength. For a confined particle, for example an electron in an atom, the wave function has the form of standing waves. Only stationary states with energies corresponding to integral numbers of wavelengths can exist; for other states the waves interfere destructively, resulting in zero probability density. Elementary examples that show mathematically how energy levels come about are the particle in a box and the quantum harmonic oscillator.

Electrons in atoms and molecules can change energy levels by emitting or absorbing a photon (light) whose energy must be exactly equal to the energy difference between the two levels. If all the electrons in an atom, ion, or molecule are at their lowest possible energy level, it and its electrons are said to be in the ground state. If an electron is at a higher energy level, it is said to be excited, or in an excited state. An electron can be excited to a higher energy level by absorbing a photon whose energy is equal to the energy difference between the levels. Conversely, an excited electron can go to a lower energy level by spontaneously emitting a photon equal to the energy difference. Since the photon's frequency is proportional to its energy, information on the energy levels and electronic structure of materials is obtained by analysing the spectrum of these emitted and absorbed photons using spectroscopy.