Question

Relation between group velocity and particle velocity

Answer 1

Relation between group and particle velocity

A material particle in motion is equivalent to a group of waves or wave packet.

The group velocity is simply the derivative of frequency ω with respect to propagation constant, from equation (1.11)

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or

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where This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program. and This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

or

This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program........(1.12)

If E and V represent the total energy and the potential energy of the particle respectively, we have

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therefore

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Using de-Broglie formula we have

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Substituting this value of in eq (1.12), group velocity will be given by

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This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

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i.e., Group velocity = particle velocity