Quantum Mechanics: Concepts and Applications · Problem 2.1

Mathematical Tools of Quantum Mechanics — Nouredine Zettili

Physics — Quantum Mechanics · linear-independence-functions

Problem

Check whether the following sets of functions are linearly independent or dependent on the real

x

-axis. (a)

f(x) = 4

g(x) = x^2

h(x) = e^{2x}

(b)

f(x) = x

g(x) = x^2

h(x) = x^3

(c)

f(x) = x

g(x) = 5x

h(x) = x^2

(d)

f(x) = 2 + x^2

g(x) = 3 - x + 4x^3

h(x) = 2x + 3x^2 - 8x^3