Hi Everybody,(adsbygoogle = window.adsbygoogle || []).push({});

I am learning solid state physics using a German book called "Festkorperphysik" written by Gross and Marx.

Now, in page 336 the Schrodinger equation in momentum space is introduced:

[tex] \left( \frac{\hbar^2 k^2}{2m} - E \right) C_\vec{k} + \sum_\vec{G} V_\vec{G} C_{\vec{k}-\vec{G}} = 0. [/tex]

Then the authors go on and say that this set of algebraic equations is a representation of the Schrodinger equation in the reciprocal space (reciprocal lattice). I guess they mean set because for each value of [itex] \vec{k}[/itex] there is one equation.

Next, they say that for each [itex] \vec{k} [/itex] there is a solution [itex] \psi_{\vec{k}} [/itex] with a corresponding energy eigenvalue [itex] E_\vec{k} [/itex].

I do not understand what [itex] \psi_{\vec{k}} [/itex] is.

From each equation I get only one value for [itex] C_\vec{k} [/itex]. And by looking at all the different values for [itex] \vec{k} [/itex] I get all the different algebraic equations from which I can extract the [itex] C_\vec{k} [/itex] with which I can construct [itex] \psi[/itex], the original wave function. That's what I thought..

Where does [itex] \psi_{\vec{k}} [/itex] come from? And related to this where does [itex] E_k [/itex] come from? Where is the eigenvalue equation that gives the k indexed wavefunction and eigenvalue?

Or is [itex] \psi_{\vec{k}} [/itex] simply given by:

[tex] \psi_{\vec{k}} = C_{\vec{k}} e^{i \vec{k} \cdot \vec{r}}?[/tex]

I do not understand.

I searched many books but didn't find any answer..

Thanks for your help in advance! :)

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Schrodinger equation in the reciprocal lattice.

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads for Schrodinger equation reciprocal |
---|

A Conductivity and Integration over Fermi-Sphere? |

I How can I obtain the reciprocal lattice of graphene? |

**Physics Forums | Science Articles, Homework Help, Discussion**