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== Explanation == [[File:Hydrogen Density Plots.png|thumb|[[Wavefunction]]s of a [[hydrogen]] atom, showing the probability of finding the electron in the space around the nucleus. Each stationary state defines a specific energy level of the atom.]] Quantized energy levels result from the wave behavior of particles, which gives a relationship between a particle's energy and its [[wavelength]]. For a confined particle such as an [[electron]] in an atom, the [[wave function]]s that have well defined energies have the form of a [[standing wave]].<ref name="Tipler"> {{cite book | last1 = Tipler | first1 = Paul A. | last2 = Mosca | first2 = Gene | title = Physics for Scientists and Engineers, 5th Ed. | publisher = W. H. Freeman and Co. | volume = 2 | date = 2004 | pages = 1129 | url = https://books.google.com/books?id=R2Nuh3Ux1AwC&dq=%22energy+level%22+%22standing+waves%22&pg=PA1129 | isbn = 0716708108 }}</ref> States having well-defined energies are called [[stationary state]]s because they are the states that do not change in time. Informally, these states correspond to a whole number of wavelengths of the [[wavefunction]] along a closed path (a path that ends where it started), such as a circular orbit around an atom, where the number of wavelengths gives the type of [[atomic orbital]] (0 for s-orbitals, 1 for p-orbitals and so on). Elementary examples that show mathematically how energy levels come about are the [[particle in a box]] and the [[quantum harmonic oscillator]]. Any [[quantum superposition|superposition]] ([[linear combination]]) of energy states is also a quantum state, but such states change with time and do not have well-defined energies. A measurement of the energy results in the [[wavefunction collapse|collapse]] of the wavefunction, which results in a new state that consists of just a single energy state. Measurement of the possible energy levels of an object is called [[spectroscopy]].
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