Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision | Last revision Both sides next revision | ||
|
hamiltonian [2016/09/08 22:48] nikolaj |
hamiltonian [2016/09/08 22:58] nikolaj |
||
|---|---|---|---|
| Line 37: | Line 37: | ||
| Up to a phase, $(e^{it\Delta_{wu}}-1)$ generates oscillations about $|\psi\rangle$. | Up to a phase, $(e^{it\Delta_{wu}}-1)$ generates oscillations about $|\psi\rangle$. | ||
| This is somewhat related to Rabi-oscillations. | This is somewhat related to Rabi-oscillations. | ||
| + | |||
| + | == On interaction terms == | ||
| + | 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". | ||
| === Reference === | === Reference === | ||
