Before Measurement It Is a Superposition
Toss a coin and cover it with your hand; until you peek it is neither heads nor tails but both as possibilities. The quantum world goes one step further. Before measurement a particle is one blended state α|↑⟩ + β|↓⟩, the up state |↑⟩ and down state |↓⟩ mixed with amplitudes α and β. In the first figure you turn the mixing angle yourself and watch the two amplitudes blend.
The notation you meet first is the ket |↑⟩ and |↓⟩, the two branch states up and down, with α and β in front as each branch's amplitude. Turn the mixing angle θ with the slider and the two bars, α = cos(θ/2) and β = sin(θ/2), grow in opposite directions. At one end it is pure |↑⟩, at the other pure |↓⟩, and in the middle a single state with both blended evenly.
A superposition shatters the instant you measure it. Press the measure button and the amplitude-blended state drops to just |↑⟩ or |↓⟩. We call this collapse. Which one appears is a probability set by the ratio of |α|² and |β|², so tilting θ toward one side with the slider makes that outcome come up more often. Because the same seed is used, the randomness is reproducible from press to press.
Where that probability comes from is told by the Born rule. The chance of getting |↑⟩ is the squared amplitude |α|², and the chance of |↓⟩ is |β|². Draw the two bars and no matter how you turn θ, their heights add to exactly 1, because the particle must land on one of the two. The key is that probability is the square of the amplitude, not the amplitude itself.
Once a state has collapsed, it stays put. Press measure to drop it to one result, |↑⟩ or |↓⟩, and measuring again right after gives the same result. Press again, and again, and it does not change. The first measurement nailed the state to that eigenstate. Press reset to return to the superposition, and only then can the outcome differ.
Finally, compare how the act of observing itself changes the state. Turn observe on and a measurement happens at every moment, pinning the state to |↑⟩ or |↓⟩ so it no longer wavers. Switch to do not observe and the superposition stays alive, its amplitudes still blended. Not looking and looking are this different. Measurement does not just read information; it changes what it touches.