Illustrated Physics
physics, drawn
Concept

Poisson distribution — where it appears

The distribution of how many independent events fall in a fixed interval when they occur at a steady mean rate. It has one parameter, its mean, and its variance equals that mean, which is why a count of N photons or decays has a fluctuation of about the square root of N.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

A bundle that swings and never spreads. A Gaussian of the ground state's own width, released at rest from x = 3 in a harmonic well and propagated on a grid by split-step Fourier, drawn at 0 of a period, 0.25 of a period, 0.5 of a period. The packet slides from side to side and its shape does not change: over 2.2 full periods the width moves by 6.6e-5 per cent, and its centre tracks x₀cos t to 8.6e-6. Every other initial width breathes. This one is the displaced ground state, and it is the closest a quantum state comes to being a classical oscillator — a definite thing at a definite place, moving on the classical trajectory, staying the size it was.

The state that swings like a pendulum

Most quantum states of an oscillator look nothing like a swinging weight. One family does: it follows the classical trajectory exactly, never spreads, and sits at the uncertainty minimum for ever — and it is the state a laser and a driven circuit actually produce.

quantum · Correspondence A loss that slides the curve and does not bend it. The same threshold of six absorbed photons with four different fractions of the light getting through the eye. On a logarithmic axis, multiplying the mean by a constant slides the curve along without changing its shape: a tenfold loss moves it by exactly one decade. So the steepness can be read off without knowing the loss at all. Hecht, Shlaer and Pirenne used this in 1942 to get a count of absorbed photons without measuring how many were absorbed.

The flash the eye counts

In 1942, three physiologists showed that a person in a dark room sees a flash only when a handful of photons are absorbed, and that each rod can respond to one. They measured no photons in the eye and no single rod. They got it from the steepness of a curve, because light arriving in lumps gives a curve whose shape does not change if most of the light is lost on the way.

quantum · Photon

Named alongside it

The objects these essays reach for when they reach for this one.

Classical limitCoherent stateCorrespondence principleHarmonic oscillatorPhotonQuantum efficiencyQuantum stateShot noiseSuperpositionUncertainty principleWave packetZero-point energy

All concepts