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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Transition dipole moment integral relation to probabilities derivation

I want to learn about selection rules and so have to understand transition dipole moment. Here is a nice text on it: https://chem.libretexts.org/Bookshelves/...
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Probability to fall back to ground state of hydrogen atom

I would like to show mathematically that electrons always fall back to ground state when in the excited state. I think that the best way would be to find the probability. Once the excited state is ...
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Probabilty Density for $x$

Suppose that I have the function $$x(t)=e^{-b(W(t))^2} \ \ \ \ \ \ \ \ (1)$$ where $W(t)$ is just a Wiener process (i.e. a Gaussian in general). I want to know what the probability density for $x$, $P(...
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Postulate of a priori probability and harmonic oscillator

According to the fundamental postulate of a priori probability in Statistical Mechanics: An isolated system in equilibrium is equally likely to be in any of its accessible states. But for a ...
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2answers
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Correct interpretation for the expectation evalue

I'm currently beginning to study QM and came across this interpretation of the expectation value in Griffiths: Quote: "It emphatically does not mean that if you measure the position of one ...
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32 views

Statistical Mechanics in rotating cylinder

I'm having trouble calculating the probability density of a particle being in a radius $r=r_0$ in a rotating cylinder. ($\omega, R, L$ are the frequency, radius, and height of the cylinder). First of ...
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Feynman Lecture 26 - Summation of Probability Amplitudes

How does Fig. 26-3 (shown below) correspond to the following paragraph from this Feynman lecture? Finally, we give a very crude view of what actually happens, how the whole thing really works, from ...
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Confusion about the canonical partition function and probabilities

I'm in a first course on statistical mechanics at the moment and I'm having trouble wrapping my head around an example problem involving the canonical partition function. The question setup has a ...
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2answers
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Quantum mechanics and rigorous math [closed]

I was reviewing a little of quantum mechanics in a rigorous way, so i realized there is a lot of concepts similar in words but different in its meanings, i would appreciate any help to understand it: ...
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Solution of the 2D stationary diffusion equation

I'm trying to find the solution to the 2D stationary diffusion equation $$-D\nabla^2P(\vec{\rho_2})=\delta(\vec{\rho_1}-\vec{\rho_2})$$ where $\vec{\rho}=(x,y)$ and $D$ is the diffusion coefficient. ...
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Probabilities to find $\psi$ in the different eigenstates of $\hat{L}_z$: how to handle the $r$-dependence?

The wave function of a particle in a spherically symmetric potential $V(r)$ is given by: $$ \psi(\vec{r})=(x+y+3z)f(r).$$ Determine the probabilities to find $\psi$ in the different eigenstates of $\...
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Parallelism between quantum density matrix and a probability distribution in classical mechanics

In quantum statistical mechanics we often define a density matrix as $\rho = \sum_{i} p_{i} | \Psi_{i} \rangle \langle \Psi_{i} | $. Its time volution is determined by the equation: $\rho \left(t\...
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What if we test three photons instead of two in Bell's paradox?

I am not a physicist and do not know anything about quantum mechanics (except that it can be formulated using Hilbert spaces), but watching a vulgarization video about Bell's paradox, I had a question ...
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A potentially flawed thought experiment

If we consider light falling on a surface seperating two media. For instance light falling on a watersurface or a normal glass window. We can exactly say that half of the photons will get transmitted ...
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Integrating a probability current

I am trying to understand how to integrate the probability current in order to get the probability of the particle moving through a certain point. I have a particle moving in a potential which is made ...
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1answer
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Determine the state $|\psi \rangle$

The question is: The angular momentum components of an atom prepared in the state $|\psi\rangle$ are measured and the following experimental probabilities are obtained: \begin{equation} P(+\hat{z}) = ...
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Transition Probability

In different fields of Quantum we talk about transition probability .for example with knowing the dynamics of a 2-levels or n-levels system people in different papers try to calculate the probability ...
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What is the Main contrast between classical coin toss and superposition state?

We know that in normal coin-toss there is two probable states HEAD OR TAIL. When we commence for measuring only get head or tail,is it means two probable states collapse into one {H or T}.in ...
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What is the probability of finding an electron in a hydrogen atom in an infinitesimal space $dV$?

I have been asked to find the most probable position of electron in infinitesimal space $dV$ orbiting a Hydrogen atom. I know that probability $P$ of finding the electron in a volume $dV$ is given by ...
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Unanswered Question on Potential Step Function

I have looked at the questions on this stack exchange and did not find a single convincing answer. Please absolutely remember the mathematical definition of only 4 things as you read this. Probability ...
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How to distinguish “chance” from simulation events?

People often like to think that given a certain probability of a dataset explaining results, like say 90%, then it implies if you "reran" events 10 times, 9 times they would return the same ...
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3answers
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Quantum model of the atom

please note that I am a high school student trying to understand the quantum model of the atom; I have only the most basic understanding of quantum mechanics. I am trying to comprehend the wave nature ...
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1answer
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Probability question based on Heisenberg's uncertainty principle?

Heisenberg's uncertainty principle relates energy and life time $\tau$ of a particle as follow: $\tau=\frac{\bar{h}}{1+x^2}$ Here energy is approximated as $1+x^2$ where $x$, the velocity of particle, ...
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Quasiconcavity of the Variance of the Gibbs Measure

Pardon me for taking some time to set up my notation as I do not come from a physics background and am not using the standard statistical mechanics notation. Consider a Gibbs measure on a set of ...
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Harmonal density Probability changes?

I have been thinking about strings vibrating. we usually see a purely elastic string in modes of vibration as states of modes. I was thinking, what if we changed the length of the string dL such that ...
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A question on probability and free fall [closed]

An object in free-fall drops from rest. The origin is at the starting point and the $y$-axis points downwards. The $y$-coordinate of the ball is, $$ y = \frac{1}{2} g t^2$$ The total time of flight is ...
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Probability distribution of atomic energy in a canonical ensemble

Imagine we have a system of atoms in the canonical (NVT) ensemble. For this system, we know that under thermal equilibrium, the probability distribution $P(E)$ of the system's total energy $E$ ...
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Probability of Finding a Quantum System in a Specific State

I know this question has likely been asked before, but I am horribly confused and need some help with this. Let's say we have a system whose initial state at t = 0 is given in terms of a complete and ...
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Question on Probability Amplitudes

The Born rule implies that the probability density $\rho$ is defined as $$\rho(x,y,z)=|\psi(x,y,z,t_0)|^2$$ at time $t_0$. What is the difference in this probability density and the probability of a ...
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What is the difference in Probability Density and probability of a particle being in a particular state?

I'm just starting to learn Quantum Mechanics, and this question is confusing me: we say that the probability of finding a particle in a state given by the Eigenstate $o_i$ is the modulus squared of ...
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Question on Probability Densities in Koopman-Von Neumann Mechanics

A book that I used to learn basic Classical Mechanics, called "No-Nonsense Classical Mechanics" by Jakob Schwichtenberg, defines the probability density in Koopman-Von Neumann Mechanics as $$...
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When an infinite square well grows from $(0, a)$ to $(0, 2a)$, why do we integrate from $0$ to $2a$?

Say we have a particle in an infinite square well where $V= \infty$ if $x<0$ or $x>a$. Then, suppose the well expanded to $V= \infty$ if $x<0$ or $x>2a$. While the wave function is ...
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Probability density in double slit experiment

I don't understand why the probability density in the double slit experiment in the case of both slits opened, has a minimum corresponding to the maximum of intensity. Shouldn't $P_{12}$ have the same ...
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Cross section of elastic scattering in repulsive central potential field

today I was studying from Landau and Goldstein and I came with this problem Cross section of elastic scattering in repulsive central potential field $U(r)=\frac{\alpha}{r}+\frac{\beta}{r^2}$, where $\...
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Qubit state probability

Consider the general qubit state $\alpha \begin{pmatrix} 0 \\ 1\end{pmatrix} + \beta \begin{pmatrix} 1 \\ 0\end{pmatrix}$ in a general orthnormal basis with vectors $\begin{pmatrix} \alpha \\ \beta \...
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Understanding difference between classical and quantum harmonic oscillator probability distributions

Here we have an example QHO wavefunction squared in blue overlayed an equivalent CHO probability distribution. I'm trying to understand intuitively why the QHO result has zeros, i.e. points where we ...
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What is meant by frequency = 0? [closed]

When I say that an event has frequency =0, does that imply that the event is impossible?
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Reversibility of Physical Process : QM vs CM

It is often stated that the processes in quantum mechanics are reversible as they follow the Schrodinger's Equation : $$ - \frac{\hbar^2}{2m} \nabla^2 \Psi(x,t) + V(x,t)\ \Psi(x,t) = i \hbar\ \frac{\...
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If the integral diverges while finding the expectation value

I was wondering what the expectation value of a wave function might be if the corresponding integral diverges. For example, if I graph the probability density $\Psi (x) = \sqrt{\lambda/\pi} \exp(-\...
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Why can't we take a limiting relative frequency over nested spheres in relativistic spacetime?

The Measure Problem of eternal inflation cosmology is to determine the correct probability measure over the theoretically infinitely many individuals (or civilizations or worlds) for self-locating ...
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Interpretation on basic results about Momentum Probability Distribution $\|\chi (k)\|$

hope you're all doing well. There might be questions related to this topic but I couldn't stand other responses mainly because I just began learning QM. There's this problem on QM1 (Quantum Mechanics ...
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Novikov self-consistency principle and probabilities?

According to the Novikov's self consistency principle (also proposed by other authors such as Kip S Thorne) 1 2, if an event exists that would cause a paradox or any "change" to the past, ...
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Griffiths QM probability problem

This isn't really a homework problem, I'm making my way through this book on my own, I've read the first couple of chapters, and have now started to do the problems but have gotten stuck on this ...
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Reconstructing field configuration from sparse data assuming a probability distribution

This question is extremely basic, so I apologise for this. Suppose we want to estimate the configuration of a field $\phi(x)$ where $x \in \Omega$, with $\Omega$ the domain. We are given the values of ...
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Probability in classical physics

I have read lots of thing on probability in QM and the different ways of intending it. Now, I am wondering how physicists intend probability in classical physics. To be more specific, I have read some ...
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How does one calculate the chance that an asteroid hits the Earth and what does this chance mean?

I read in this article (in "Independent"): An asteroid that is projected to come close to Earth later this year has a 0.41 percent chance of hitting the planet, according to Nasa data. The ...
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Should we trust quantum mechanics for working of the mirrors?

In this video, it is explained that it is not necessary that photons obey the laws of reflection and each photon can take any possible path to reach the so-called black hole receiver and all the paths ...
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What is the Majorana wavefunction in Kitaev chain?

Considering $N$ particle Kitaev chain in the topological phase, if we solve the 2N$\times$2N BdG Hamiltonian matrix,we can get zero energy eigenvalue, and two corresponding degeneracy state in the ...
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Significance of Wronskian appearing in particle flux

When we derive the expression for particle flux/probability current, we find that it is directly proportional to the Wronskian of $\psi$ and its conjugate and deduce that it is constant when particle ...
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Is there a minimum “Planck” probability analog of the minimum Planck distance? [closed]

I know the Planck distance is real, but is there a Planck probability? I know the wavefunction units is length to the negative 3/2 number of particles. So can we calculate a minimum probability from ...

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