Just an idea: is there an index theorem for an n-dimensional Hamiltonian(adsbygoogle = window.adsbygoogle || []).push({});

[tex] H = -\triangle^{(n)} + V(x)[/tex]

which "counts" the bound states

[tex] (H - E) \,u_E(x) = 0[/tex]

i.e. eigenfunctions and eigenvalues in the discrete spectrum of H?

**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!

# Number of bound states and index theorems in quantum mechanics?

Loading...

Similar Threads for Number bound states | Date |
---|---|

I Measurement of the mean value of the number of photons? | Saturday at 1:44 AM |

A Field quantization and photon number operator | Mar 27, 2018 |

I Complex numbers of QM | Feb 14, 2018 |

I Is this a Stirling number of the second kind? | Dec 27, 2017 |

Energies and numbers of bound states in finite potential well | Apr 5, 2013 |

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