Posted by Steve Simon on March 25, 2013, 1:20 pm, in reply to "Re: Page 255, Mott antiferromagnetism"
You are correct. The word "amplitude" is not used carefully enough here. The hopping has dimensions of energy. In perturbation theory for the wavefunction, one gets back a real amplitude because there is an energy denominator as well. So, if one were doing perturbation theory for the wavefunction, it would read as state> = 0> + sum_n n> The numerator, has a matrix element with value (what i called "amplitude") t. But then the dimensions work out because of the denominator. I think this abuse of nomenclature is common. Strictly it is only an amplitude once the energy denominator is included. 
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