What is Bloch theorem and Kramers theorem and can you take each example showing the theorem...

What is Bloch theorem and Kramers theorem and can you take each example showing the theorem clearly?

Expert Solution

Bloch theorem :

It states that "energy eigenstates of an electron in a crystal can be written as Bloch waves. Bloch theorem states that the electron wavefunctions in a crystal have a basis consisting entirely of Bloch wave energy eigenstates."

Where , = Bloch wave

u = Periodic function

k = Crystal wave vector

e = Euler number

i = imaginary unit

Example :

A periodic dielectric in electromagnetism leads to photonic crystals.
A periodic acoustic medium leads to phononic crystals

Kramers Theorem :

It states that "for every energy eigenstate of a time reversal symmetric system with half integer total spin , there is atleast one more eigenstate with the same energy."

Example :

The deuterium (D) isotope contains an neutron with proton and electron so that the total number of fermions is three and the theorem can be applied.
The hydrogen atom (H) contains one proton and one electron , hence the theorem can not be applied.

genius_generous answered 2 weeks ago

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