Abstract
We consider a hierarchy of Hamilton operators Ĥ N in finite dimensional Hilbert spaces $$ \mathbb{C}^{2^N } $$. We show that the eigenstates of Ĥ N are fully entangled for N even. We also calculate the unitary operator U N(t) = exp(—Ĥ N t/ħ) for the time evolution and show that unentangled states can be transformed into entangled states using this operator. We also investigate energy level crossing for this hierarchy of Hamilton operators.
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