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Calculate eigenenergy splitting present at Brillouin zone

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Reference no: EM131814802

Exercise -

The eigenstates of electrons in a periodic potential are described by Bloch waves. Each Bloch factor has to obey the respective differential equation

1319_figure.png

Please prove -

(a) The Kramer's degeneracy (valid for same band index σ) εσ(k→) = εσ(-k →), and

(b) The relation εσ'(k→ + K→h→) = εσ(k→) and the property for the set of Bloch waves

1954_figure1.png

(c) Calculate the eigenenergy splitting present at the Brillouin zone boundaries via the Bloch wave solutions valid in a case of a weak potential modulation felt by the electrons.

Reference no: EM131814802

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