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.

Filter by
Sorted by
Tagged with
0 votes
1 answer
30 views

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 ...
user avatar
  • 3,813
-1 votes
1 answer
39 views

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^{...
user avatar
0 votes
0 answers
31 views

Coherent States of a Harmonic Oscillator [closed]

I have used the definitions of the annihilation and creation operators to determine the coherent state of a harmonic oscillator. I have derived the equation $$|\alpha \rangle=e^{\frac{-\alpha^{2}}{2}}\...
user avatar
0 votes
0 answers
25 views

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 ...
user avatar
  • 404
0 votes
0 answers
34 views

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 ...
user avatar
1 vote
0 answers
74 views

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 ...
user avatar
  • 5,499
0 votes
1 answer
43 views

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 ...
user avatar
0 votes
0 answers
47 views

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 ...
user avatar
  • 1,027
1 vote
1 answer
32 views

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 ...
0 votes
1 answer
48 views

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 ...
user avatar
  • 3,813
13 votes
1 answer
1k views

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 ...
user avatar
1 vote
0 answers
15 views

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 ...
user avatar
1 vote
0 answers
40 views

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....
user avatar
  • 219
0 votes
0 answers
27 views

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 ...
user avatar
  • 219
1 vote
1 answer
97 views

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 ...
user avatar
0 votes
2 answers
80 views

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 ...
user avatar
0 votes
1 answer
29 views

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.
user avatar
2 votes
0 answers
73 views

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 ...
user avatar
0 votes
0 answers
16 views

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 ...
user avatar
0 votes
1 answer
44 views

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 ...
user avatar
0 votes
0 answers
16 views

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 ...
user avatar
0 votes
2 answers
61 views

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 ...
user avatar
  • 41
1 vote
1 answer
40 views

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|\...
user avatar
2 votes
2 answers
123 views

Unit of a log normal probability density function

How do I find the unit of a log-normal probability density function?
user avatar
0 votes
0 answers
30 views

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-...
user avatar
3 votes
3 answers
120 views

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 ...
user avatar
  • 131
1 vote
1 answer
58 views

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 ...
user avatar
  • 25
0 votes
2 answers
59 views

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 ...
user avatar
  • 688
3 votes
1 answer
125 views

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 ...
user avatar
1 vote
1 answer
43 views

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 ...
user avatar
  • 13
3 votes
1 answer
113 views

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^...
user avatar
-1 votes
2 answers
101 views

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?
user avatar
  • 15
2 votes
1 answer
52 views

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/...
user avatar
1 vote
0 answers
115 views

Why doesn't Gleason's theorem imply the Born rule?

I know that the question "does Born's rule follow from Gleason's theorem" has already answers on the website: see here, and here. I am not satisfied with the answers given (one cannot rule ...
user avatar
  • 409
0 votes
1 answer
49 views

How do I get photon probabillity from electromagnetic potentials?

I have a question about probabillity of photon from electromagnetic fields. We know that electromagnetic four-potential, which can be found with QED equations $A_{\mu}=\bigl(\begin{smallmatrix}\frac{\...
user avatar
1 vote
1 answer
89 views

Gibbs entropy maximization confusion with Grand Canonical Ensemble

I'm trying to review some statistical mechanics from the following link In doing so on the topic of variational theory and maximization with Lagrange multipliers, the author states that given a ...
user avatar
  • 203
2 votes
3 answers
144 views

Why is $e^{i(kx - \omega t)}$ a valid wave function since it isn't finitely integrable on $\Bbb R$?

Why is $\psi = e^{i(kx - \omega t)}$ a valid wavefunction since it isn't finitely integrable on $\Bbb R$? I'm studying derivations of the Schrödinger Equation, which start with a simple wave function ...
user avatar
0 votes
2 answers
92 views

Why particularly probability density is defined as $|\Psi|^2=\Psi \Psi^{*}$?

It may be a stupid question, but why particularly for probability density expression $k~|\Psi|^2 = k~\Psi^{*}\Psi$, it's assumed that $k=1$? As it is now, then in a complex plane probability density ...
user avatar
3 votes
3 answers
64 views

How to understand electron trajectories in a probabilistic model?

I recently stumbled upon the definition of a Relativistic particle: A relativistic particle is a particle which moves with a relativistic speed; that is, a speed ...
user avatar
  • 143
1 vote
1 answer
31 views

Is the integral of the probability density of finding a paricle symmetric about the mean?

Is the probability density integral of finding a particle symmetric about the expectation value? Also is the probability integral symmetric with respect to standard deviations from the mean? Like if I ...
user avatar
1 vote
0 answers
47 views

Do virtual particles have a density?

I am currently working with some theory that predicts that virtual particles would have a higher density (higher chance of appearing) in strong gravity field and would move towards gravity force. I ...
user avatar
1 vote
2 answers
53 views

Prove that entropy increases with the number of states

According to the formulation of entropy as $$S = -\sum_i P(i)\log(P(i))\quad,$$ how do we know that entropy increases with the number of states of a system regardless of their probability distribution?...
user avatar
0 votes
1 answer
56 views

Computing $\langle x\rangle$ for state in infinite potential well [closed]

We are given a state $$\psi(x)=\frac{1}{\sqrt{2}}(\phi_1(x)+\phi_3(x))$$ where the $\phi_i$'s are eigenstates corresponding to the infinite potential well case. I was wondering if $$\langle x \rangle=\...
user avatar
1 vote
0 answers
46 views

Quenched and annealed disorder in a combinatorial problem

For a research project I'm dealing with a combinatorial problem which I am modeling as a disordered system. For some context, the problem is the TSP, and the disorder enters through the weights on its ...
user avatar
1 vote
3 answers
209 views

Spherical harmonics and Bra-Ket notation

Let's assume i have a wave function $$\psi = N(x+y+z)e^{-r^2/a^2} $$ with $N$ and $a$ some constants. This function can be written as a sum of the spherical harmonix $Y_{1,0}$, $Y_{1,1}$ and $Y_{1,-1}$...
user avatar
1 vote
1 answer
79 views

Probability of Finding an Electron Close to the Nucleus of a Hydrogen Atom

I am trying to calculate the probability of finding an electron in a small volume element close to the nucleus of a ground state hydrogen atom. I then need to calculate the same but replacing the ...
user avatar
  • 167
0 votes
1 answer
46 views

The probability density function for the double-slit experiment

I am desperate. I've scoured the web for the formula for the probability density function for the interference pattern obtained in the double slit experiment with both slits open. So I want to know ...
user avatar
  • 1
0 votes
1 answer
25 views

Conceptualizing time series data of fluctuating sizes of particle aggregates

I am working with simulation data (a time series of positions) of aggregating particles. I want to look at the overall distribution of aggregate size. A colleague calculated the number of aggregates ...
user avatar
0 votes
0 answers
21 views

Probability of finding the electron of a hydrogen atom within a cone of a given angle

I am working on a question where I must find "the probability of an electron being located within a cone of semi-angle 20 degrees w.r.t the z-axis" for the 2s and 2p states of a Hydrogen ...
user avatar
  • 167
2 votes
1 answer
64 views

What do $R(r)$ , $R^2(r)$ & $4\pi r^2 R^2(r) $ represent in accordance to schrodinger's wave equation?

What do $R(r)$ , $R^2(r)$ & $4\pi r^2 R^2(r) $ represent in accordance to schrodinger's wave equation? Being a JEE aspirant I haven't been taught to properly interpret the Schrodinger's wave ...
user avatar

1
2 3 4 5
24