Calculating the frequency of a free electron

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The discussion focuses on the calculation of a free electron's frequency using two different equations, leading to a discrepancy involving a factor of two. The user initially derives the frequency using momentum and wavelength, resulting in f = mv²/h, while a second approach using energy leads to f = mv²/2h. The difference is attributed to the distinction between phase and group velocities of the electron. Clarification is needed on which velocity is being referenced for accurate calculations. Understanding this difference is crucial for resolving the factor of two issue.
Turukano26
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I feel like I must be missing something obvious, but I can't figure it out. I have the speed of an electron, and to calculate its frequency i used p = h/λ, then subbed in p =mv and λ= v/f. Giving me the equation f = mv2/h. However, I also could use E = 1/2 mv2 and E = hf to give me the equation f = mv2/2h. Where is this factor of two coming from??
 
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I am not entirely sure, but I think you have discovered the difference between phase and group velocities of the free electron.And, they are different. Griffiths has a great section on this (Griffiths "Introduction to Quantum Mechanics", Sec 2.4, Eq. 2.90).

Before proceeding you must tell us which "speed" do you mean. The phase velocity, or the group velocity.
 
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