# Differences

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hamiltonian [2016/09/08 22:58] nikolaj |
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Say we start with a model $W$ and eigenstates $|w\rangle$, $|u\rangle$ and then decide to make it "more realistic" and add interaction terms, making for a new Hamiltonian $W'$. Usually $W'=W+qI$, where $q\in{\mathbb R}$ is a scalar called couple constant. One now said this describes an interacting system, but that's a relative notion: All Hamiltonians like $W$ or $W'$ that one considers are hermitean and thus diagonalizable, i.e. there are states $|w'\rangle$, $|u'\rangle$ for $W'$ which are not interacting. The nomenclature basically just comes from sticking to the old states and this is mostly done because those are the ones one can compare. | Say we start with a model $W$ and eigenstates $|w\rangle$, $|u\rangle$ and then decide to make it "more realistic" and add interaction terms, making for a new Hamiltonian $W'$. Usually $W'=W+qI$, where $q\in{\mathbb R}$ is a scalar called couple constant. One now said this describes an interacting system, but that's a relative notion: All Hamiltonians like $W$ or $W'$ that one considers are hermitean and thus diagonalizable, i.e. there are states $|w'\rangle$, $|u'\rangle$ for $W'$ which are not interacting. The nomenclature basically just comes from sticking to the old states and this is mostly done because those are the ones one can compare. | ||

- | So given a system with $W'$ is e.g. in an eigenstate $|u'\rangle$ with oscillation frequency $u'$ ("total energy of the system"), then expressed as superposition of $|w\rangle$ and $|u\rangle$ we have a notion of total energy flowing between those non-eigenstates of the "interacting system". | + | So given a system with $W'$ is e.g. in an eigenstate $|u'\rangle$ with oscillation frequency $u'$ ("total energy of the system"), then expressed as superposition of $|w\rangle$ and $|u\rangle$ (making for a state that undergoes an back and forth according to $\Delta_{wu}$) we have a notion of total energy flowing between those non-eigenstates of the "interacting system". |

=== Reference === | === Reference === |