Exercise 2: Using the Relativistic Energy Momentum relationship ?2 = ?2?2 + ?2?4 and the de-Broglie...

Exercise 2: Using the Relativistic Energy Momentum relationship ?² = ?²?² + ?²?⁴ and the de-Broglie relationships ? = ℏ? and ? = ℏ? with ? the angular frequency and ? the wave number, find the group ?_? and the phase velocity ?_?ℎ of the de-Broglie waves and show that their product is equal to ?².

Expert Solution

Given the energy momentum relationship

And the de Brogile relationships

we have



  The group velocity is defined as





And the ohase velocity is defined as

And so,
we have the product of the phase velocity and the group velocity as

genius_generous answered 2 years ago

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