Hilbert space, a sonnet

Lee Herron
Haverford College, 2003

We've studied oscillators big and small
With pendulum and breathing modes embraced
But there's another way to grasp it all,
With normal modes as vectors in a space.
This inner product space holds many keys.
Where basis vectors sum to give us clues
'Bout how to wield our normal modes with ease,
And thus, solutions to our Diff. EQs.
Used often in describing quantum states,
Indeed a daunting subject it subtends.
But with the vector math it correlates,
One sees its usefulness needs no defense.
Without it, where we'd be, I cannot place.
Its name, known far and wide, is Hilbert Space.