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