|ψ(x)|²
A particle is a wave of amplitudes
Until it is measured, an electron has no single position. It has an amplitude at every place, the wavefunction ψ, and |ψ|² is the chance of finding it there. A qubit is the simplest case: just two amplitudes, α for 0 and β for 1.
↗ + ↙ = 0
Amplitudes can cancel
Probabilities only ever add up. Amplitudes are arrows with a direction, called the phase, so they can also cancel. That is why electrons make interference fringes, why some barriers turn see-through, and how quantum algorithms make wrong answers disappear.
E₁ < E₂ < E₃
Trapped waves come in steps
A wave confined to a region can only take shapes that fit, so its energy comes in steps: the “quantum” in quantum mechanics. It explains the sharp colours atoms emit, and why a trapped particle can never sit perfectly still.