Quantum Physics

    

Propagation of a Wave Packet in a Dispersive and Dissipative Medium

Authors: Marcello Colozzo

The propagation of a wave packet in a dispersive and dissipative medium is really complicated. We limit ourselves to an analysis deriving from series expansions truncated to the first order. We will start from a one-dimensional De Broglie wave packet relating to two special cases: 1) free particle; 2) particle in a periodic potential. In these two cases we will refute the assertion according to which the energy is transported with the group velocity, since the observable energy is not defined (the wave packet is a superposition of eigenfunctions of the energy). We will show however that the expectation value of the energy is transported with the group velocity.The conclusions can be immediately generalized to the propagation of a packet of electromagnetic waves in a dispersive and dissipative medium, justifying the expression group delay of a wave packet.

Comments: 7 Pages.

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Submission history

[v1] 2024-10-21 09:21:20

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