I'm writing a report for a computer lab where we ran simulations of the wavefunction of an electron in an array of square wells as per the Kronig-Penney model and i'm just looking for some verification of my interpretation of Bloch's Theorem as it applies to the solutions of the schrodinger equation in this case.(adsbygoogle = window.adsbygoogle || []).push({});

2. Relevant equations

ψ_k (x)=u_k (x)e^ikx , solution to the SE for the periodic potential.

My understanding of it is that the e^ikx is the 'envelope' for the solution and takes the shape of the solution of the SE for an equivalent single well and the u_k(x) is the periodic function that modulates the wavefunction with the same periodicity of the lattice.

So for the lower energy band, is the envelope function the familiar 1/2 wave for all states in the lower band and the 1 wavelength wavfunction the envelope for all the states in the higher band?

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# Bloch functions in Kronig-Penney model

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