(adsbygoogle = window.adsbygoogle || []).push({}); Free Electron Model: Why periodic boundary conditions and what is "L"?

Right, hello!

The quantum free electron model for electrons in solids (in One dimension) says we need to use periodic boundary conditions such that if Y(x) is the wavefunction, then Y(x) = Y(x+L).

Where L seems to be the width of the infinite square potential well used to derive the wavefunction and associated energy eigenvalues.

Now I realise that the periodic boundary conditions relates to the periodic lattice but, if L is the length of the 1D metal, then surely x+L is outside of the metal?

If L actually relates to some very small length inside the lattice, perhaps the size of a unit cell, then why when deriving the Fermi Energy do we use n=N/L where N is the total number of electrons in the metal and n is the number per unit length.

So my question really is, what is "L"?

Thanks

PS how do I use greek and other symbols here?

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# Free Electron Model: Why periodic boundary conditions and what is L ?

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