# Energy level

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A quantum mechanical system or particle that is bound -- that is, confined spatially-- can only take on certain discrete values of energy. This contrasts with classical particles, which can have any energy. These discrete 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.

If the same energy level is shared by more than one quantum mechanical state, energy levels are " degenerate ". They are then called degenerate energy levels.

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### Explanation

Quantized energy levels result from the relation between a particle's energy and its wavelength. For a confined particle such as 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.