So­lu­tion schrod­sol-a


The en­ergy of a pho­ton is $\hbar\omega$ where $\omega$ is the clas­si­cal fre­quency of the elec­tro­mag­netic field pro­duced by the pho­ton. So what is $e^{-{{\rm i}}E_{{\vec n}}t/\hbar}$ for a pho­ton? Are you sur­prised by the re­sult?


The ex­po­nen­tial $e^{-{{\rm i}}E_{{\vec n}}t/\hbar}$ be­comes $e^{-{\rm i}{\omega}t}$. That is the clas­si­cal time de­pen­dence of the elec­tro­mag­netic field.

The re­sult is not re­ally sur­pris­ing, be­cause of the wave-par­ti­cle du­al­ism of quan­tum me­chan­ics. Clas­si­cal physics un­der­stands the wave na­ture of light well, and not its par­ti­cle na­ture. This is the op­po­site of the sit­u­a­tion for an elec­tron, where clas­si­cal physics un­der­stands the par­ti­cle na­ture, and not the wave na­ture.