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I went to a review session today where the TA basically described the hamiltonian as a variable. In the example problem he gave, it told you what the variable stood for (it was a derived equation) and you simply plugged the given equation into Schrodinger's equation and then defined the variables in the equation, no solving necessary!
In terms of the Hamiltonian in the context of the midterm, the variable itself is given on the formula sheet I believe, so for the purpose of the midterm, all you really have to know is the basic format of the Schroedinger equation: H(wavefunction)=E(wavefunction) and then just plug in the variable from the formula sheet into H.
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