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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The probability of a circular region being "invaded" by moving spheres as a function of time

I had uploaded the same problem in maths stack exchange but since it got no answer and because I think that it is a problem that can be seen both as a physical one I considered uploading it both on ...
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Why do some factorized states have different probability than others in terms of Clebsch-Gordan coefficients?

When adding a spin-1 to a spin-1/2, we have a six-dimensional Hilbert space spanned by the factorized states $$ \left \{ \left | j_1=1, m_1 \right \rangle \otimes \left |j_2= \frac{1}{2}, m_2 \right \...
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Confusion about Feynman rules for free photon propagation

In the book (and lecture series) "QED", Feynman gives a recipe for calculating the amplitude that a photon emitted from point A would be detected at point C. The recipe is to sum the ...
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(Classical) Probability distribution of momentum for a harmonic oscillator (Griffiths problem 1.12)

I am trying to solve problem 1.12 in Griffith's Introduction to Quantum Mechanics, but when I compare my answer to the solutions online it is wrong. We want to find the probability distribution of ...
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Why do I see $\frac{1}{\sqrt2}$ a lot in QM?

A lot of books and papers in QM use $\frac{1}{\sqrt2}$ in equations. If we want to calculate the intensity of a light or some probability, I see this irrational value every where. why do we use this ...
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Probability in the Multiverse Interpretation of Quantum Mechanics [duplicate]

The Multiverse Interpretation of Quantum Mechanics interprets a quantum decision as different universes, each with each outcome. I was wondering how probability plays into this. For example, if we ...
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What is the probability of a three-body collision for a thousand particles Gaussianly sampled and trapped in a harmonic potential?

I know, the title is confusing because it's put probably badly . Here is the scenario: A thousand particles each with initial conditions $(x_0,p_0)$ such that $x_0$ and $p_0$ are sampled from two ...
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Quantum state from probability [closed]

Is it possible to determine a quantum state given the probabilities of +/- in the x and y components. For example, a quantum state $|\psi\rangle$ has the following probabailites: \begin{equation} \...
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Does the Planck limit on the probability density of wave functions have any measurable effect?

The probability density of wave functions is an inverse volume. If the smallest measurable volume is the Planck volume defined with the Planck length using $V_{min}=l_{Pl}^3$, then there is a maximum ...
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Particle decay in Everett's many-worlds interpretation (MWI) - is it probabilistic?

I've watched Sean Carroll videos where he describes how to use Everett's many-worlds interpretation (MWI) for e.g. https://en.wikipedia.org/wiki/Schr%C3%B6dinger%27s_cat. Superposition of one particle'...
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Fokker-Planck: uniqueness and convergence to stationary distribution

Consider the Langevin equation ($N$-dimensional) with nonlinear drift term, but expressible as a gradient of a function $U(\vec{x})$. Namely, consider the stochastic process described by the set of ...
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Interpretation of Born Rule In QFT

Can we born rule be used to find probability of a particle to exist in a region in QFT using the formula $\int_a^b \psi(x)\psi^*(x)dx$,where $\psi(x)$ is a fermionic field? If yes, please provide ...
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QM - Shooting photons at a certain point until they hit a particle

Given some probability distribution $\rho(x)$ of a particle, say I wanted to check if the particle is located at some point between $x$ and $x+\Delta x$, If I were to continuously shoot photons at ...
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Wavefunction Amplitude Intuition

Reading the responses to this question: Contradiction in my understanding of wavefunction in finite potential well it seems people are pretty confident that, e.g., the wavefunction of a particle in a ...
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Double slit experiment: how to derive the figure of interference?

We know that by performing the Double Slit Experiment we get an interference pattern on the detector screen. To explain this most sources talk about the state of the particle: calling $|\psi _l \...
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Calculation of the mean value of energy in a wave function: proving that $\langle E \rangle_\psi = \sum_i P(E_i) E_i$

Let a wave function $\displaystyle \Psi(x) \equiv \frac{1}{Z}\sum_{i=1}^n \psi_i(x)$ with $n, Z \in \mathbb{R^+_0}$ such as $\displaystyle ||\Psi(x)||^2 \equiv \int_\mathbb{R} \Psi^\star(x).\Psi(x) \ ...
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How to find the probability current density of hydrogen atom wave function?

Can someone give me a book recommendation or a pdf where I can find how to get the radial, polar and azimuth component of it? I try to do it myself but I can't really figure out what to do next,
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"Forbidden nodes" of a quantum particle trapped in a harmonic oscillator potential

Let's consider a confinant potential $V(x) \in C^2(\mathbb{R}, \mathbb{R})$, of the form of a harmonic oscillator ($V(x) = x^2$ for example): Consider a classical particle which has a kinetic energy $...
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Probability of observing harmonic oscillator at a particular position

Consider a classical harmonic oscillator whose Hamiltonian is $$H=\frac{p^2}{2m} +\frac{1}{2}mw^2x^2$$ where $w$ is the oscillating frequency. I wish to find the probability of observing the harmonic ...
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Probabilities of eigenfunctions

I am struggling to understand how to get the probabilities of each eigenstate occurring from a wavefunction that is a linear combination of eigenfunctions. If we have a wavefunction $$\Psi = A ( e^{...
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Quantum measuring simulation

Hi I want to understand a concept that I been thinking about. I'm trying to simulate the energy measurement of a system (a many body quantum system to be precise), and I'm trying to simulate a quantum ...
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What is an intuitive or simple proof of Gleason's theorem and how it relates to the Born rule?

What is an intuitive or simple proof of Gleason's theorem and how it relates to the Born rule? I tried to read the articles, but the proof seemed big and the kind that are unintuitive (im not ...
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Can this shape of matrix elements in the path integral formalism be linked to some sort of expectation value?

This question is about expressions of the form $$ \langle x_f, t_i | \hat{x}(t) | x_i, t_i \rangle = \frac{1}{N} \int_{x(t_i) = x_i}^{x(t_f) = x_f} \mathcal{D} x~x(t)e^{i S[x]}. $$ In the following ...
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Why sum of squares of the magnitudes of Fourier coefficients in Infinite Square Well equals one but it is not so in regular Fourier analysis?

My question is basically this.. In regular math, Fourier Coefficients give the "amount" a particular frequency is available in any periodic signal. The squares of sum of coefficients is not ...
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Why is there a non-zero probability density of finding an $l=0$ electron at the origin of a Hydrogen-like atom?

A well known result for the $l=0$ hydrogenic functions is that $$\psi_{nlm_l}=R_{nl}(r)Y_{lm_l}$$ $$|\psi_{n00}|^2=\frac{Z^3}{\pi a_0^3n^3}$$ where $R_{nl}$ and $Y_{lm_l}$ are the radial function and ...
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Neutrino Oscillation and Probability

I am a fresher in a university pursuing physics major. I have been very passionate about neutrinos. So, I started studying them. But I have realised that, it requires a lot of mathematical physics ...
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Integrate continuity equation in QM

From Shankar's QM book pg. 166: The continuity equation for probability density in QM is $$\frac{\partial P(\vec{r},t)}{\partial t}=-\nabla \cdot \vec{j}(\vec{r},t),$$ where $P=\psi^*\psi$ is the ...
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If frequency of photons is a continuous spectrum, wouldn't the chance of a photon having the exact right frequency to excite an electron be zero?

As far as I'm aware, the energy needed to excite an electron to a different orbital is discrete. Since the frequency of light is continuous, wouldn't it be impossible for a photon to have the exact ...
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What is the probability distribution of the density of a random part of vaccuum?

If I understand correctly the vaccuum fluctuates and has a zero point energy. Because of Heisenberg Uncertainty principle the density of a random part of vaccuum cannot be zero. So imagine if you have ...
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Expression of density operator for Microcanonical ensemble

Consider a quantum microcanonical ensemble,with a fixed energy $E$. In Greiner, the expression for its density operator is given as. $\displaystyle\hat\rho=\frac{\delta(\hat H-E.1)}{Tr(\delta(\hat H-E....
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Conservation of flux in scattering problem

Consider a localised potential which becomes 0 after some distance $a$. So, we are considering a wave coming from infinity along z direction, so for $r>>a$, $\psi_{incoming}=e^{ikz}$ Now for ...
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Why not imaginary eigenvalues in the eigenvalue equation $A\psi=\lambda\psi$?

in quantum mechanics we always see the eigenvalue equation $\hat A\psi=\lambda\psi$ and $\lambda$ is the probability amplitude meaning $\lambda^2$ is the actual probability of finding the system in ...
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Is there a lower bound on probability where we can say an event is impossible? [closed]

So I was studying quantum mechanics and I came upon this table that shows the probability (T) of a given particle tunneling through a potential barrier. And the last value $10^{-628}$ made me think ...
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How can I calculate the probability of Neutrino hiting in a certain detector?

I was looking through the DUNE experiment. And it led me to think, If there's way to calculate or do probability where the neutrino might hit in a large chunk of matter in a given neutrino beam rate.
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What is the probability that a random walk forms (almost) a circle?

Given is a random walk of a particle in 3d (such as an atom in a liquid). The particle proceeds randomly (in 3d), with an average straight displacement length a. Is there a way to get a probability ...
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We know that nodes are regions where the probability of finding an electron is zero right? [duplicate]

According to the text I'm going through it says, that the probability density has always some value howsoever small it may be at finite distance from the nucleus. So this means that the probability of ...
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Do annealed energies underestimate quenched energies?

In the physics of disordered systems, there are two ways to treat the disorder: Quenched disorder, in which the disordered variables are considered to be frozen with respect to the thermodynamic ...
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Is there a formula for probability of Compton Scattering?

I am making a Monte Carlo simulation of an X-ray detector and trying to account for Compton Scattering, but cannot find anywhere a formula for the probability that Compton Scattering occurs, only that ...
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What type of probability distribution, Gaussian, Poisson, etc, does time independent wavefunction or $|Ψ|²$ usually take, or is it completely random?

What shape the probability distribution for finding a particular particle in 3D space usually takes at any given time, for free particles not subject to any external influence? and does this shape ...
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Probability for scattering event

I am reading Schwartz QFT. On page 61 in eq (5.20) he gives an expression that describes the probability for a $2\to n$ scattering event to happen: $$dP=\frac{T}{V}\frac{1}{(2E_1)(2 E_2)}\left|\...
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Unit of a log normal probability density function

How do I find the unit of a log-normal probability density function?
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Rate Dispersion is the distribution of rates on a rate spectrum. What are the quantities physically associated in a Rate Spectrum?

I am working on a project to decipher the "origin of rate dispersion" arriving because of Heterogeneity in our system using correlation function analysis in Python. Rate Dispersion, non-...
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3 votes
3 answers
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Why can’t quantum randomness be understood as epistemic? [duplicate]

I often hear people say that quantum randomness is “true randomness”, but I don’t really understand it. Please bear with my question. Before the development of quantum physics, randomness is ...
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Molecule collision probability

In a time $dt$ , our molecule will sweep out a volume $\sigma vdt$.If another molecule happens to lick inside this volume, there will be a collision.With $n$ molecules per unit volume, the probability ...
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Probability in a small interval is $P. dx$

Reif says ... variable $u$ which can assume any value in the continuous range $a_{1}<u<a_{2}$. To give a probability description of such a situation, one can focus attention on any ...
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Kardar: The derivation of the Maxwell Boltzmann distribution function

In Mehran Kardar's volume 1: Statistical Physics of Particles, he introduces the Maxwell Boltzmann distribution function just after the discussion on the microcanonical ensemble as follows: The joint ...
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How to scale Poissonian light?

In quantum optics, coherent light with constant frequency, phase, and amplitude shows poissonian photon number statistics: $$P(n) = \frac{\bar{n}^{n}}{n!}e^{-\bar{n}}.$$ A well-known result for ...
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Probability more than 1 when integrating the Electron density in Density functional theory

The electron density used in density functional theory for a system of $N$ electrons with wavefunction $\psi$ is defined as $$\rho(r)=N\int \Psi^*(r,r_2,\dots r_N)\Psi(r,r_2,\dots r_N) d^3r_2\dots d^...
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Intuitive meaning of Yang-Mills

Is it fair to say that the "new" thing about Yang-Mills equations is that they "bend" the probability amplitude locally like mass bends space in general relativity?
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2 votes
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Normalizable, but singular distribution

I have obtained a probability distribution for the observable $l$ which takes the form: $$ \frac{dP}{dl}=\frac{(1-\sqrt{1-3l^{2}})^{2}}{l^{3}\sqrt{1-3l^{2}}}\exp\left[-\frac{4\pi}{9l^{2}}(1-3l^{2})^{3/...
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