Questions tagged [probability]
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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Drake Equation with Random Walks
Goal
I'd like to use the Drake Equation with random walk theory to estimate the probability of aliens reaching Earth.
Drake Equation
The Drake Equation estimates the number of advanced civilizations ...
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Can self-indication assumption solve the fermi paradox? [closed]
Consider $P$ the probability that our civilization appears from beginning to the end. $P$ should also be the probability that at least 1 extraterestrial civilization exists. If we asses that $P$ is 50%...
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Probabilistic curvature of spacetime [duplicate]
I was wondering since matter tells space-time how to curve, and since matter is probabilistic in position (say hydrogen atom) is the curvature also probabilistic?
black holes slowly shrink by ...
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Quantum Mechanical Current Normalisation
Consider an electron leaving a metal. The quantum-mechanical current operator, is given (Landau and Lifshitz, 1974) by
$$
j_x\left[\psi_{\mathrm{f}}\right]=\frac{\hbar i}{2 m}\left(\psi_{\mathrm{f}} \...
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What is the physical meaning of the normalization of the propagator in quantum mechanics?
Suppose we have a quantum field theory (QFT) for a scalar field $\phi$ with vacuum state $|\Omega\rangle$. Then, in units where $\hbar = 1$, we postulate that the vacuum expectation value (VEV) of any ...
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What Does Feynman Mean When He Says Amplitude and Probabilities?
In Feynman lectures on gravitation section 1.4, he tries to debate over whether one should quantize the gravitation or not.
He provides a two-slit diffraction experiment with a gravity detector, which ...
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Quantum: Which improbable macroscopic events are possible?
Basically, the title. Web search had not found pages in top results with similar QA.
E.g. I understand nuclear blast can just end at any time because random chain-reaction has probability of not ...
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Probabilistic behavior of quantum mechanics [closed]
In a hypothetical scenario, if I were to measure the quantum spin of an electron and it showed "up," and then I traveled back in time without changing the initial conditions, would measuring ...
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Is the zero vector necessary to do quantum mechanics?
Textbook quantum mechanics describes systems as Hilbert spaces $\mathcal{H}$, states as unit vectors $\psi \in \mathcal{H}$, and observables as operators $O: \mathcal{H} \to \mathcal{H}$. Ultimately, ...
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Physical meaning of each term of the square modulus of a wave function
The expression below is the square modulus of the wave function of a harmonic potential ($V=\frac{1}{2}m\omega^2 x^2$) in which it's stated that the probability of finding the particle in the $\psi_0$ ...
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Factorization on increments in Markov chain
I'm trying to show the following property for a Markov chain:
$$\left<[x(t+\tau)-x(t)][x(t'+\tau)-x(t')]\right> =\left<x(t+\tau)-x(t)\right>\left<x(t'+\tau)-x(t')\right> $$
Where $t\...
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Boltzmann distributions on atomic orbitals: infinite degeneracy?
The (unnormalized) Boltzmann probability distribution of states as a function of energy and temperature is given by
$$P(\epsilon_i) \propto g_i\exp\left(\frac{-\epsilon_i}{k_BT}\right)$$
with $P(\...
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What is the connection between moments in probability theory and the moment of inertia?
My question arises as the moment of inertia (MOI) has been described as a second moment.
In my understanding if the MOI is indeed a second moment of a distribution of mass, this suggests the MOI could ...
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Fermi's Golden Rule: Interpreting the Dirac Delta in Transition Probabilities [duplicate]
I am trying to understand an aspect of Fermi's golden rule in the case of a constant perturbation, $V$. The formula for the transition probability from an initial state $i$ to a final state $f$ is ...
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Is there a name for the number of '9's in numbers such as 0.999 (where it would be 3)?
I am doing an optics simulation involving transmission and reflection coefficients very close to 1, such as 0.999. While I was an undergraduate student, a professor mentioned that, in certain fields, ...
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