Is the direction of a photon's momentum uncertain when emitted from an atom?

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SUMMARY

The discussion centers on the emission of photons from atoms, specifically addressing the uncertainty of a photon's momentum direction when emitted from a hydrogen atom. It is established that while the magnitude of the photon's momentum is precisely defined as p = hf/c, the direction of that momentum remains uncertain due to the spherical symmetry of the wavefunction. The conversation references Einstein's concept of "needle-like radiation" and emphasizes the wave-particle duality of photons, highlighting that although the emission probability is uniform in all directions, the photon ultimately travels in a single direction upon emission.

PREREQUISITES
  • Quantum mechanics fundamentals
  • Understanding of wave-particle duality
  • Knowledge of photon momentum calculations (p = hf/c)
  • Familiarity with the concept of wavefunctions
NEXT STEPS
  • Research the implications of spherical symmetry in quantum mechanics
  • Study the concept of wavefunction collapse during photon emission
  • Explore Einstein's theories on the Photoelectric Effect
  • Learn about the Heisenberg Uncertainty Principle in the context of momentum and position
USEFUL FOR

Physicists, quantum mechanics students, and anyone interested in the behavior of light and photons in atomic processes.

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Classically, a pulse of light emitted by an atom would be viewed as an electromagnetic wave radiating spherically symmetrically out from the atom. Quantum mechanically speaking, if say a hydrogen atom emits a single photon, does the photon's wavefunction spread out spherically, us having no idea on which side of the we will detect it? Also, am I correct in assuming that we know the magnitude of the photon's momentum exactly (p = hf/c), in which case the uncertainty in its momentum is all uncertainty about the direction of its momentum? Clarification about this situation would be great, because I haven't been able to been able to find anywhere which deals it fully.
 
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For an atom in a spherically symmetric state the amplitude for the photon to be emitted is equal in all directions. But, when the photon is actually emitted, it only goes in one direction. In Einstein's paper on the Photoelectric Effect he wrote of "needle-like radiation".
 
the momentum is h/lambda... the photon is considered a wave "package" and can be calculated as such...
 

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