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hamiltonian [2016/09/08 22:58]
nikolaj
hamiltonian [2016/09/08 23:00] (current)
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 ===
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