Quantum Mechanics (1) · Problem 5

A few things first

Physics — Quantum Mechanics · scalar-products-function-spaces

Problem

Consider the (real) vector space of real continuous functions with continuous first derivatives in the closed interval [0,1][0, 1]. Which of the following defines a scalar product? (a) ⟨f∣g⟩=∫01f′(x)g′(x) dx+f(0)g(0)\langle f|g\rangle = \int_0^1 f'(x)g'(x)\,dx + f(0)g(0) (b) ⟨f∣g⟩=∫01f′(x)g′(x) dx\langle f|g\rangle = \int_0^1 f'(x)g'(x)\,dx

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