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]

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# Can a Hamiltonian be unbounded ?

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