Is a Free Electron in an Electric Field Still Free?

AI Thread Summary
A free electron in an electric field is no longer considered free, as its momentum changes due to the influence of the field. The relationship p = hbar k does not hold in this context, leading to variations in kinetic momentum. The specific effects depend on the type of electric field, such as uniform or Coulomb fields, and the nature of the problem being analyzed, whether it involves stationary states or transitions. Consequently, the electron's behavior and momentum become uncertain in the presence of an electric field. The discussion highlights the complexities of electron dynamics under external forces.
Niles
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Hi all

Is a free electron (with momentum p = hbar k) still free if it is in an electric field? I.e., is the momentum is given as p = hbar k?
 
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No, it is not free any more. No, the kinetic momentum is different and may well be uncertain because there is no k any more. It depends on the form of the external electric field: uniform, Coulomb, etc., as well as on the problem you solve: stationary states or transitions.
 
Last edited:
Hi there,

Under the action of an electric field, the momentum of a free electron will vary.

Cheers
 

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