Dear all,(adsbygoogle = window.adsbygoogle || []).push({});

I am doing summer research in the field of Molecular Quantum Electro Dynamics, and a persistent problem that I (and occasionally the group I am working with) have/has is knowing what to use as the density of final states (radiation states).

It is required in the Fermi Golden Rule, when calculating a rate:

[tex]\Gamma={{2\pi}\over{\hbar}}|M_{fi}|^2\rho[/tex]

The most accepted definition in all the textbooks I can find is:

[tex] \rho={{k^2d\Omega}\over{(2\pi)^3{\hbar}c}}V [/tex]

Which is useful, except for in two circumstances:

1) When there is not a well defined quantisation volume (i.e. all of space)

2) When we wish to consider one single direction, so cannot integrate over solid angles

Does anyone here know how to deal with these situations, or of an alternative, more useful, definition?

I have tried solving 1) by choosing an appropriate quantisation volume, but the answer one gets is rather dependent upon the volume chosen.

I have seen a book solve 2) by forming an intensity of emitted radiation instead of a rate, but this is of no use for my purposes (an intensity includes units [tex]m^{-2}[/tex], making it impossible to recover a rate in [tex]s^{-1}[/tex] because a single direction has zero area).

I have tried to solve 2) by invoking uncertainty principles, but this is a bit hand waving and not very rigorous.

Thank you all in advance

Scott

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

Dismiss Notice

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!

# Density of States

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads for Density States | Date |
---|---|

A States in usual QM/QFT and in the algebraic approach | Feb 14, 2018 |

A Von Neumann Entropy of a joint state | Jan 17, 2018 |

I Qubit mixed state density matrix coordinates on a Bloch ball | Feb 23, 2017 |

I On uniqueness of density matrix description as mixed state | Jan 10, 2017 |

I The Lagrangian of a Coherent State | Jul 8, 2016 |

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