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 | Science Articles, Homework Help, Discussion**

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?

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