Question

Question 1 (a) Use a theorem from vector calculus to show that for a conventionally-normalised energy eigenfunction, that is one that obeys fd3r Ψ = 1 as well as HYe = EVE, where we have adopted the usual phase convention that energy eigenfunctions are real-valued. The integral on the RHS is called the "energy functional (b) Now consider small variations around a true energy eigenfunction, that is perform the replacement in the energy functional, subject to the constrant that the varied wave func- tion is still conventionally normalised i.e Show that the change in the energy functional vanishes to first order in δΨΕ By looking up what "calculus of variations" means, or just by nutting it out yourself explain the mathematical significance of this result

Answer 1

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