Transition Probability - Fiber

This is the probability that a quantum state will transition to another quantum state, and is also called the transition probability. For example, an atom in a high-energy state will transition to a lower-energy state as a result of the electrons in the atom interacting with an electromagnetic field. In this case, the transition probability per unit time is given by (2π/ħ)| h _ab | ² ρ, where h is the matrix element _related to the states a and b of the electrons before and after the operator that gives the interaction between the electron and the electromagnetic field, and ρ is the number of states after taking into account the state of the emitted light. Here, ħ = h /2π ( h is Planck's constant). If energy is not conserved before and after the transition, this probability is zero.

In general, when a quantum state a transitions to another stationary state b due to an action that causes a state transition, this is also called the transition probability, but the transition probability is not necessarily proportional to the square of the absolute value of the matrix element of the action. In the example of an electron in an atom given above, this is because the interaction between the electron and the electromagnetic field that causes this action is weak.

[Hajime Tanaka]

Source: Shogakukan Encyclopedia Nipponica About Encyclopedia Nipponica Information | Legend

量子的状態が他の量子的状態に移っていく確率のことで、転移確率ともいう。たとえばエネルギーの高い状態にある原子は原子内電子が電磁場と相互作用し、その結果エネルギーの低い状態に移っていく。この場合の単位時間当りの遷移確率は、電子と電磁場の相互作用を与える演算子の、前後の電子の状態a・bに関する行列要素をh_ab、放射される光の状態も考慮したあとの状態の数をρとすれば(2π/ħ)|h_ab|²ρで与えられる。ただし、ħ=h/2π（hはプランク定数）。遷移前後でエネルギーが保存されない場合のこの確率はゼロとなる。

　一般に量子的状態aが状態の遷移を引き起こす作用によって他の定常状態bに遷移していく場合も遷移確率というが、遷移確率はかならずしも作用の行列要素の絶対値の2乗に比例するとは限らない。先にあげた原子内電子の例は、この作用に与える電子と電磁場の相互作用が弱いためである。

［田中　一］

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