- #1
zetafunction
- 391
- 0
the idea is can a Hamiltonian in 1-D of the form [tex] H=p^2 + V(x) [/tex] for a certain function V(x) be unbounded and have NEGATIVE energies , for example a Hamiltonian whose spectra may be [tex] E_{n} = ...,-3,-2,-1,1,2,3,... [/tex] and so on, so we have an UNBOUNDED Hamiltonian with positive and negative energies with the property
[tex] E_{-n}=-E_{n} [/tex]
[tex] E_{-n}=-E_{n} [/tex]