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 - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Can a Hamiltonian be unbounded ?

Loading...

Similar Threads - Hamiltonian unbounded | Date |
---|---|

I Hamiltonian in Schrödinger: necessarily total energy? | Feb 22, 2018 |

I Why the second quantization Hamiltonian works? | Feb 21, 2018 |

I Representing a Hamiltonian in an operator form | Feb 5, 2018 |

Unbounded Hamiltonian leading to finite ground state | Dec 28, 2013 |

Is the harmonic oscillator Hamiltonian an unbounded operator? | Nov 18, 2010 |

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