Question

relationship between group velocity and particle velocity

Answer 1

A group velocity of matter wave is given by
V group = dw / dk
where w = 2πv and k = 2π / λ

From Planck’s equation E = hv and from de Broglie wavelength, we can write
λ = h/p

Using the above equations, we rewrite the expressions for w and k.

w = 2πE / h & k = 2πp / h

Now, differentiating the expressions for w and k, we get

dw = 2π / h dE & dk = 2π / h dp

Substituting the expressions for dw and dk into the v group equation,

V group = dw / dk = 2π / h. dE // 2π / h. dp

V group = dE / dp

Since we are dealing with the matter-waves E can be the kinetic energy of particle in wave
motion.

Using the relation E = p² / 2m and differtiating it with respect to p, we get

V group = dE / dp = 2p / 2m. = p / m


From the definition of particle velocity,

V particle = p / m

∴ V group = V particle

Answer 2

Answer:

what is relation between group velocity and partical velocity