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Statement of a problem № 3499

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The relation for total energy E and momentum p for a relativistic particle is E^2 = c^2p^2 + m^2c^4 , where m is the rest mass and c is the velocity of light. Using the relations, E = hw and p = hk, where w is the angular frequency and k is the wave number and h= h/2pi , h being Planck's constant. Show that the product of group velocity vg and the phase velocity vp , vp·vg = c^2 .

Solution:
The relation for total energy E and momentum p for a relativistic particle is E^

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