# Tagged Questions

For questions about probability, probability theory, probability distributions, expected values and related matters. Purely mathematical questions should be asked on Math.SE.

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### Why is the probability of finding a particle in a quantum well greatest at its center?

Imagine that in a classical sense, a particle has some total energy $E$ and that its potential energy $U(x)$ varies with $x$ in the shape of a well (see the top-left image). Of all the possible ...
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### Probability in Measuring Noncommuting Observables

If I have a particle in a state $\Psi(x) = e^{-x^2}$ could I calculate probability of simultaneously measuring, say, $x > 0, p_x < 0$? I understand that $p_x$ and $x$ don't commute and cannot ...
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### How can I make this toy quantum random walk model unitary?

Take a toy $(1+1)$-dimensional lattice model of the universe. A particle begins at $x=0$ at $t=0$. It has an amplitude ${1}/{\sqrt{2}}$ to move one step to the left and amplitude ${1}/{\sqrt{2}}$ to ...
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### Earth still exists - does this fact tell us anything about LHC safety?

When LHC was about to be launched there were many fears that it would destroy the world. To counter them scientists tried to carefully examine all possibilities and concluded that there is nothing ...
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### Problem with momentum values in a QM problem

I have the following equation of $Ψ$ around a ring (the particle is bound to move only on the ring): To visualize the state(it dies before L/2 if L=2πR): We can see from the first picture that ...
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### Can binary sequences generated from ergodic maps be chaotic?

Briefly, the way symbols are generated is: Consider a one-dimensional chaotic map $T: [0,1]→[0,1]$ and a time series $\{x_n\}_{n=1}^N$ generated with this map. Define a threshold $A$ and a ...
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### Importance of local conservation of probability

In almost every textbook of quantum mechanics we can find the derivation of the local conservation of probability. $$\nabla\cdot\vec{J}+\partial_t (\psi^*\psi)=0$$ where $\vec{J}$ is probabilty ...