energy level

1. The energy characteristic of a stationary state of a physical system, especially a quantum mechanical system.
2. The stationary state of a quantum mechanical system.

One of the allowed values of the internal energy of an isolated physical system. This energy is not free to vary continuously above its minimum value, as predicted by classical mechanics, but is constrained to lie among a set or spectrum of particular values. This spectrum may consist of both an isolated discrete portion and a continuous component of restricted range. The term energy level usually refers to one of the allowed values in the discrete set.

The primary indication for the existence of discrete energy levels came from the study of the spectrum of emissions of energetically excited atomic systems. Historically, the most important such spectrum is that of the simplest atom, hydrogen, a system of one proton and one electron bound together by their electromagnetic attraction. Within the framework of classical physics, the structure of the hydrogen atom poses fundamental problems. The first is the existence of a stable ground state: An electron in orbit around a proton is in constant acceleration, and therefore, according to Maxwell's classical electromagnetic theory, should continuously radiate away energy. Furthermore, the radiation emitted as the atom decays to a lower energy state should form a continuous spectrum of frequencies. However, the hydrogen atom both possesses a stable ground state and emits radiation at only a discrete set of frequencies.

In 1913 N. Bohr made a fundamental advance by postulating that the angular momentum of the electron-proton system could take on only a discrete set of values. The angular momentum is said to be quantized. A consequence is that the excitation energies of the hydrogen atom also have a discrete spectrum. Bohr made the further postulate that the atom decays from an excited level, E_k, only by making a transition to a lower energy level, E_j, emitting a single light quantum (photon) in the process. The energy, E_γ, of this photon is given by the conservation of energy, E_γ = E_k − E_j. Although Bohr's postulates are in many ways without real foundation, they were later justified and extended by the development of quantum mechanics. See also Atomic structure and spectra.

The quantization of the allowed energy values that occurs in quantum mechanics has analogs for other physical quantities as well, such as angular momentum. The basic reason why such quantization occurs for bound systems of particles in quantum mechanics but not in classical mechanics is that in quantum mechanics particles have associated wavelike attributes, specifically a wave function which encodes the dynamical state of the particle. (This is the content of wave-particle duality.) The wave function of a bound state satisfies an equation similar in many ways to the equation describing waves on a guitar string or drumhead of finite extent. Such musical instruments produce only certain specific notes, or frequencies, for a given length of string or size of drumhead. In other words, the frequencies are quantized. Similarly, the modes of oscillation of the wave function for a quantum system of finite extent are also quantized, leading to discrete energy levels, and so forth. An unbound quantum system, however, is analogous to a string of infinite length, which can play a continuous range of notes.

Energy levels are of great importance for many systems other than simple atoms such as hydrogen. For instance, they determine the interactions and binding of molecules in chemistry and biochemistry, the stability or decay of nuclei, and the macroscopic properties of solids, such as the optical properties of dyes or semiconductors. The observed spectroscopy of the energy levels of a system can also elucidate the properties of a new force, just as the study of hydrogen led to the development of quantum mechanics and quantum field theory.

The noun has one meaning:

Meaning #1: a definite stable energy that a physical system can have; used especially of the state of electrons in atoms or molecules
  Synonym: energy state

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