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

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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

Answer: Option D

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