Bloch theorem derivation - David Miller

[@राम-म7फ]

Thanks for the explanation

[@SharadaNagarkar-fu8du]

clearest explanation I saw about Bloch thm, thank you! One question although, in the visualization, you have shown envelope to be a wave with different periodicity than 'a'. What does this wave represent? In case is just represents the 'cos'(real) part of this term, then where is the 'sine' part? And what is the physical interpretation of e^ikx? , it cannot be an EM wave because magnitude of EM wave is not always 1 at every single point, right? The derivation is based on the assumption that magitude of this term e^ikx is always 1. So going ahead, we cannot neglect the 'sine' component of it, is that correct?

[@davidmillerquantum]

You are right I am only showing the "cos" part, just for graphic simplicity. The "sine" part would have the same kind of behavior, but just shifted sideways. This wave is a quantum mechanical wave, so it can be complex. EM waves are often modeled for mathematical convenience as being complex waves, but then we take the real part at the end to get back to the actual physical wave. In quantum mechanics, we have to be prepared to retain the full complex wave, however. Whether that complex wave has any real "meaning" is a good question; in practice, it is better just to use it as a way of performing calculations of things like probability densities (which involve the modulus squared of the final quantum mechanical wave). And, indeed, for full calculations we would have to deal with the "sine" part also in quantum mechanics, which we can easily do.

[@vimladwivedi4407]

Thankyou for the explaination

[@brandonwashington4422]

Awesome video thanks!