Editing Adiabatic theorem (section)

=== Comparison with the adiabatic concept in thermodynamics ===
The term "adiabatic" is traditionally used in [[thermodynamics]] to describe processes without the exchange of heat between system and environment (see [[adiabatic process]]), more precisely these processes are usually faster than the timescale of heat exchange. (For example, a pressure wave is adiabatic with respect to a heat wave, which is not adiabatic.) Adiabatic in the context of thermodynamics is often used as a synonym for fast process.

The [[Classical mechanics|classical]] and [[Quantum mechanics|quantum]] mechanics definition<ref name=Griffiths>{{cite book |last=Griffiths |first=David J. |title=Introduction to Quantum Mechanics |year=2005 |publisher=Pearson Prentice Hall |isbn=0-13-111892-7 |chapter=10 }}</ref> is instead closer to the thermodynamical concept of a [[quasistatic process]], which are processes that are almost always at equilibrium (i.e. that are slower than the internal energy exchange interactions time scales, namely a "normal" atmospheric heat wave is quasi-static, and a pressure wave is not). Adiabatic in the context of mechanics is often used as a synonym for slow process.

In the quantum world adiabatic means for example that the time scale of electrons and photon interactions is much faster or almost instantaneous with respect to the average time scale of electrons and photon propagation. Therefore, we can model the interactions as a piece of continuous propagation of electrons and photons (i.e. states at equilibrium) plus a quantum jump between states (i.e. instantaneous).

The adiabatic theorem in this heuristic context tells essentially that quantum jumps are preferably avoided, and the system tries to conserve the state and the quantum numbers.<ref name=":1">{{cite web |author=Zwiebach |first=Barton |date=Spring 2018 |title=L15.2 Classical adiabatic invariant |url=https://www.youtube.com/watch?v=qxBhW2DRnPg&t=254s?t=03m00s |url-status=live |archive-url=https://ghostarchive.org/varchive/youtube/20211221/qxBhW2DRnPg |archive-date=2021-12-21 |publisher=MIT 8.06 Quantum Physics III}}{{cbignore}}</ref>

The quantum mechanical concept of adiabatic is related to [[adiabatic invariant]], it is often used in the [[old quantum theory]] and has no direct relation with heat exchange.