Principles of Quantum Mechanics · Problem 1.1.3

Mathematical Introduction — R. Shankar

Physics — Quantum Mechanics · linear-vector-spaces

Problem

Do functions that vanish at the end points

x = 0

and

x = L

form a vector space? How about periodic functions obeying

f(0) = f(L)

? How about functions that obey

f(0) = 4

? If the functions do not qualify, list the things that go wrong.