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Wave Packets1 Page 62 Definition Assert that k0 , x0 f k k exp ik x x dk (1.1) 0 0 Let y=k-k0 k0 , x0 f y exp i y k x x dy (1.2) 0 0 Evaluate the integral in accordance with ..\..\definitions\AiGau\GuidingFunction.docx So that k0 , x0 20 20 exp i t i 1 i ko x x0 Is a packet at x0. Group velocity Uses the fact that in free space w = ck E x, t f k k exp ik x x iwt dk 0 0 f k k exp ik x x 0 0 ct dk (2.1) Suppose w is a function of k E x, t f k k exp ik x x iw k t dk (2.2) 0 0 The maximum of the packet occurs when the exponential has an extremum. This occurs when 1 David Bohm, Quantum Theory, Prentice Hall (1951) pp 60-70 ik x x0 iw k t k (2.3) or x x0 t 0 w k k This is the velocity of the maximum of the wave packet.