Question

с V A wave packet describes a particle having momentum p. Starting with the relativistic relationship E2 = p2c2 + Eo?, show that the group velocity is ßc and the phase velocity is where ß = ). How can the phase velocity physically be greater than c? The group velocity of a wave is represented by ugr dE which gives the following expression. (Use the following as necessary: C, P, and Eo.) Ugr dE dp The phase velocity of a wave is represented by Vph = if which, in terms of momentum and angular frequency, gives the following expression. (Use the following as necessary: n, p, and w.) Vph = if = We substitute E into the expression and rewrite vph as follows. (Use the following as necessary: E and p.) Vph

Answer 1

0 Guren, & pro + Co. expo V Group velocity Upx - de nich 2 E de 2 x 28 dp. 9 EdE e p dp op Ugr d dp TA E c²mv me² v=Bc a foc (as Bar ugs. Upea or 2 & Upha Ugr ßc. & Uph a B from 0 Ugs C c as e lugs, Upa - Upay C. (prored) Mgra de from JA Рc- op & prce + Uph = 2 f = x W h Р tw ho QoP सा Upt a [as E = hw P P