Introduction to Quantum Mechanics · Problem 3.2

Formalism — David J. Griffiths

Physics — Quantum Mechanics · hilbert_space

Problem

(a) For what range of ν\nu is the function f(x)=xνf(x) = x^\nu in Hilbert space, on the interval (0,1)(0, 1)? Assume ν\nu is real, but not necessarily positive. (b) For the specific case ν=1/2\nu = 1/2, is f(x)f(x) in this Hilbert space? What about xf(x)x f(x)? How about (d/dx)f(x)(d/dx) f(x)?

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