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Hi. A very quick question. Why is it impossible for a wave to travel on a linear one-atomic chain if its wavelength equals the lattice constant? I.e. the lattice points vibrate with a wavelength equal to the distance between them? Here's what I mean:

http://www.lcst-cn.org/Solid%20State%20Physics/Ch42.files/image020.gif [Broken]

http://www.lcst-cn.org/Solid%20State%20Physics/Ch42.html [Broken]

The dispersion relation says that the "wave" will have zero frequency if the wavelength equals the lattice constant.

I can see why it must be so mathematically, but I can't understand intuitively why this must happen.

http://www.lcst-cn.org/Solid%20State%20Physics/Ch42.files/image020.gif [Broken]

http://www.lcst-cn.org/Solid%20State%20Physics/Ch42.html [Broken]

The dispersion relation says that the "wave" will have zero frequency if the wavelength equals the lattice constant.

I can see why it must be so mathematically, but I can't understand intuitively why this must happen.

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