[tex](adsbygoogle = window.adsbygoogle || []).push({});

V(x) = \left\{\begin{array}{ll}

0, & \exists n\in\mathbb{Z},\; x\in [2nL, (2n+1)L]\\

\infty, &\exists n\in\mathbb{Z},\; x\in\; ](2n-1)L, 2nL[\\

\end{array}\right.

[/tex]

This is a periodic potential. L is some constant. Is a solution

[tex]

\psi(x) = \chi_{[0,L]}(x)\;\sin\big(\frac{\pi x}{L}\big)

[/tex]

of the Schrödinger's equation

[tex]

\Big(-\frac{\hbar^2}{2m}\partial_x^2 + V(x)\Big)\psi(x) = E\psi(x)

[/tex]

a counter example to the Bloch's theorem?

[tex]\chi_{[0,L]}[/tex] is a characteristic function, 1 when [tex]x\in [0,L][/tex] and 0 otherwise.

**Physics Forums - The Fusion of Science and Community**

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!

# Counter example to the Bloch's theorem?

Loading...

Similar Threads - Counter example Bloch's | Date |
---|---|

Superposition in relation to Counter factual definiteness | Jan 25, 2016 |

QFT counter-terms | Jan 9, 2016 |

Young's Double Slit Experiment with Single Photon Counters and Offset Mask | Oct 5, 2012 |

What's wrong with this local realistic counter-example to Bell's theorem? | Feb 22, 2011 |

QFT Counter Terms example calculation? | Jul 1, 2010 |

**Physics Forums - The Fusion of Science and Community**