Verify that a freely moving electron cannot spontaneously emit or absorb a photon.

Name: Problem 21, Chapter 7: Introduction to modern physics
Uploaded: 2021-10-27T19:03:10-08:00
Duration: 4 min 37 s
Channel: Arpit Gupta
Description: Verify that a freely moving electron cannot spontaneously emit or absorb a photon.

step 1 In this question we have to verify that a freely moving electron can't spontaneously emit or abs

Verify that a freely moving electron cannot spontaneously...

Key Concepts

Conservation of Energy and Momentum

In any physical process, the total energy and momentum before and after the event must be conserved. This principle is fundamental in both classical and quantum physics. When analyzing a free electron emitting or absorbing a photon, applying these conservation laws shows that there is no way to balance the energy and momentum simultaneously. Any attempt to do so leads to a contradiction, thereby forbidding the process under normal conditions.

Relativistic Kinematics and Mass Shell Conditions

Relativistic kinematics introduces the energy-momentum relation (or mass shell condition) which for a particle with mass states that E² = p²c² + m²c?, while for a photon, a massless particle, the condition simplifies to E = pc. When a free electron, which obeys the massive particle relation, hypothetically emits or absorbs a photon, reconciling these differing dispersion relations under the umbrella of four-momentum conservation becomes impossible. This mismatch is the core reason why such spontaneous emission or absorption cannot occur for a free electron.

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