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

[tex] E_{-n}=-E_{n} [/tex]

**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!

# Can a Hamiltonian be unbounded ?

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