Probability distributions are much less daunting than their names suggests. In the end, they just describe how probable certain outcomes are. In [[Quantum Mechanics|quantum physics]], they appear both in the continuous and the discrete case. Here, we will focus on the discrete case for simplicity. Imagine a coin with two sides, heads and tails. If you were to bet with a friend, you are interested in throwing a fair coin, i.e. heads and tails are equally probable. In other words, in 50% of the cases the coin shows heads, in the other 50% tails. When throwing the coin 150 times, that corresponds to roughly 75 heads and 75 tails (with a bit of error due to statistics). By plotting these numbers, we get the diagram below. If the coin is biased towards tails, we might see the left plot. ![[coin_probability_distribution.excalidraw.light.svg]] Coin tossing and [[Quantum Mechanics|quantum mechanics]] have more in common than we might initially think: the [[Schrödinger Equation|Schrödinger equation]] predicts the probability distribution of all outcomes in [[Quantum Mechanics|quantum mechanics]] [[Determinism|deterministically]], i.e. we know the probability distribution. Just as we know the distribution for a fair coin. However, we cannot predict the outcome of the next [[Measurement|measurement]], just as we cannot predict the outcome of the next coin toss. >[!read]- Further Reading >- [[Quantum State]] >- [[Superposition]] >- [[Quantum is completely random]] >- -[[Determinism]] >[!ref]- References