When an excited state couples to the vacuum, it has an infinite number of directions of the quantized electromagnetic field to couple to. Does it evolve into a superposition of all those directions at the same time and only collapses once the photon is measured, or does it couple to only one? (Or, of course, is there no experimental way to tell?)
From what I know/understand, the spontaneous emission should conserve the energy, momentum, total angular momentum, etc. Therefore, you could extract the momentum of the photon from the conservation laws. In particular, it might have the same dirrection as the $$ inner product, where of course, $\psi$ is the excited state and $|0>$ the "ground state" or the state on which the transition is made.
Dear Hossein Jafarzadeh,
I would say it definitely should couple to ALL of them; hence should it be in a supeposition of states.
Only when detected in one direction then it wil "collapse" to one channel.
Maybe with weak interactions/measurements one could probe this.
Something like this was done in experimentally creating W-like states with spontaneos decay. I guess the group around J. von Zanthier in Erlangen was involved in this.
Sincerely Yours,
Andreas Osterloh
The wave function expands in all directions. It collapses into one direction when it is detected. There is no way to show this experimentally.
Little correction for previous comment. Wave function is usually solution of Dirac or Schrodinger equations. Electromagnetic waves represent solutions of D'Alembert equation.
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