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If you use a test function in the variational method, you will get an upper bound for the th energy provided that is orthogonal to

If you use a test function in the variational method, you will get an upper bound for the th energy provided that is orthogonal to the lowest 1 energy states.

a. Prove that this is the case

b. How might we guess trial functions that are guaranteed to be orthogonal to some set of eigenstates, without knowing the exact eigenstates in advance?

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