# 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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### Mapping monoenergetic dose rates to a dose rate from a spectrum of neutron energies [closed]

I have the following function N(E) = B Sinh(sqrt(2E)) e^(-0.88E) which represents the release of fission neutrons over different energies. I have calculated dose rates for different monoenergetic ...
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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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### Normalizing Propagators (Path Integrals)

In the context of quantum mechanics via path integrals the normalization of the propagator as $$\left | \int d x K(x,t;x_0,t_0) \right |^2 ~=~ 1\tag{1}$$ is incorrect. But why? It gives the correct ...
1 vote
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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, ...
1 vote
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### Interpretation of a probability that does not normalize to one in stat mech?

I am trying to understand the meaning of the "n-particle distribution function" as defined by the three references below([1][2][3]), primarily those by Claudio Zannoni. Setup: For a system ...
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### How to compute classical probability distribution for 1D harmonic oscillator with $K/x$ (central force) potential energy?

I am trying to find, or derive, the probability distribution function for a classical 1D harmonic oscillator with a $K/x$ potential energy (from a $K/x^2$ central force). I am familiar with the ...
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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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### 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, ...
1 vote
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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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### How are quantum systems different from dice?

I've had this question for a while: Is a state space $\mathcal{H}$ for a quantum system just a sample space in a probability space? The question arises because i can't really tell a difference between ...
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### Why the transition probability in the master equation approach just the rate$*dt$ for a simple birth process?

I am modeling a process of an exponentially growing population of cells as $\frac{dn}{dt}=\lambda n$. To account for the intrinsic noise in the birth process of these cells, I write down the ...
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1 vote
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### How can you test to see if a dice is weighted?

I was browsing Etsy today and came across this. What tests are there to see if the dice are usable, ie, if one side isn't favored over another, and if all sides are balanced? Would this just be to ...
1 vote
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### The role of probability in the many-worlds interpretation [duplicate]

A quantum system can transition to one of two states, with probabilities 30% and 70%. The many worlds interpretation says that the universe splits into two, one for each state. If so, what do the 30% ...
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### Ornstein–Uhlenbeck process: joint probability as a Gaussian

The problem Consider a stochastic process with the following three properties: The process is Markov, meaning that $p(x_n,t_n|x_{n-1},t_{n-1},\ldots x_1, t_1) = p(x_n,t_n|x_{n-1},t_{n-1}).$ The ...
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### How is the inner product of two quantum states related to their associated Bloch vectors?

I have a doubt about how two equivalent ways of calculating the inner product between two states seem to not be actually equivalent, as they should. In particular, I'm interested in the case where the ...
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### Fermi-Dirac Distribution for Multiple Species

If I have a system containing two types of fermions, what is the probability of a state of energy $E$ being occupied? Is it just the sum of two standard Fermi probabilities for each type of fermion?
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### How to go from probability distribution to transitions probability distribution?

For the past few days I have been studying Advanced statistical mechanics. I am studying a Wiener process in general. Such a process is a non-stationaty time-independent Gaussian process. The ...
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### A question about time evolution of position distributions

If I have two probability distributions $P$ at $t$ and $P’$ at $t’$ separated by some time interval. Then, can I describe the transform between the two distributions as P’(x) = \int P(a) D(a, x-a, t’...
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### Probability amplitude in Layman's Terms

What I understood is that probability amplitude is the square root of the probability of finding an electron around a nucleus, but the square root of the probability does not mean anything in the ...
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### How would one calculate the actual probability of a macro event given what we know of physics?

Suppose I wanted to calculate the “true” probability of me tossing a coin tomorrow and it landing on heads. Now, even though we often say that this is 50%, correct me if I’m wrong, but this can’t be ...
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### Statistical independence of $x,y,z$ dimensions for Maxwell velocity distribution function

I have been looking into the derivation of the Maxwell speed distribution function as for instance given in https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution#...
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### Why do the Schrödinger and Dirac equations contain the mass?

I know the Schrödinger equation is bascially the "quantized" Hamiltonian formalism from classical mechanics, and the Dirac equation is the special-relativistic version. But these equations ...
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### Is there an equivalent of a Galton box for a converging probability?

This is a question about probability. The Galton box (or quincunx) uses the physical process of shot moving down a pin-board, to demonstrate central limit theorem, eg: So I am interested in events ...
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### Where is my mistake in using a measurement operator instead of Born’s rule to calculate the probability of detecting photons at an arbitrary angle?

As I asked in this question: https://quantumcomputing.stackexchange.com/questions/36998/how-can-i-calculate-the-measuring-probabilities-of-a-two-qubit-state-along-a-cer/37000#37000 From here I know ...