The Bloch theorem states that within a crystal, the wave function ( overrightarrow bfr ) , of an electron has the form

( overrightarrow bfr ) = u( overrightarrow bfr )e^i.overrightarrow bfk .overrightarrow bfr where, u( overrightarrow bfr ) = u( overrightarrow bfr + overrightarrow bfA ),overrightarrow bfA is a lattice vector and overrightarrow bfk is an arbitrary vector

This question belongs to Engineering Physics Solid State Physics

Solid State Physics

The Bloch theorem states that within a crystal, the wave function $$\psi \left( {\overrightarrow {\bf{r}} } \right)$$ , of an electron has the form

A) $$\psi \left( {\overrightarrow {\bf{r}} } \right) = u\left( {\overrightarrow {\bf{r}} } \right){e^{i.\overrightarrow {\bf{k}} .\overrightarrow {\bf{r}} }}$$ where, $$u\left( {\overrightarrow {\bf{r}} } \right)$$ is an arbitrary function and $$\overrightarrow {\bf{k}} $$ is an arbitrary vector B) $$\psi \left( {\overrightarrow {\bf{r}} } \right) = u\left( {\overrightarrow {\bf{r}} } \right){e^{i.\overrightarrow {\bf{G}} .\overrightarrow {\bf{r}} }}$$ where, $$u\left( {\overrightarrow {\bf{r}} } \right)$$ is an arbitrary function and $$\overrightarrow {\bf{G}} $$ is a reciprocal lattice vector C) $$\psi \left( {\overrightarrow {\bf{r}} } \right) = u\left( {\overrightarrow {\bf{r}} } \right){e^{i.\overrightarrow {\bf{G}} .\overrightarrow {\bf{r}} }}$$ where $$u\left( {\overrightarrow {\bf{r}} } \right) = u\left( {\overrightarrow {\bf{r}} + \overrightarrow {\bf{A}} } \right),\,\overrightarrow {\bf{A}} $$ is a lattice and $$\overrightarrow {\bf{G}} $$ is a reciprocal lattice vector D) $$\psi \left( {\overrightarrow {\bf{r}} } \right) = u\left( {\overrightarrow {\bf{r}} } \right){e^{i.\overrightarrow {\bf{k}} .\overrightarrow {\bf{r}} }}$$ where, $$u\left( {\overrightarrow {\bf{r}} } \right) = u\left( {\overrightarrow {\bf{r}} + \overrightarrow {\bf{A}} } \right),\,\overrightarrow {\bf{A}} $$ is a lattice vector and $$\overrightarrow {\bf{k}} $$ is an arbitrary vector

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Correct Answer: Option D

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The Bloch theorem states that within a crystal the wave function...

The Bloch theorem states that within a crystal, the wave function $$\psi \left( {\overrightarrow {\bf{r}} } \right)$$ , of an electron has the form

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