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hamiltonian [2016/09/08 22:48]
hamiltonian [2016/09/08 22:58]
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 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 ===
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