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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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Ehrenfest theorem and correlation among observables at the quantum scale

I am studying quantum mechanics and I encountered the famous Ehrenfest Theorem, which states that given an observable $A$, its expectation value time evolution is governed by $\partial_t\langle A\...
2
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1answer
211 views

Calculating average quantities in kinetic theory

Consider a volume $V$ with $5$ particles each of mass $m$ at positions $\mathbf{q}_i=(x_i,y_i,z_i) \in V$ and with velocities $\mathbf{v}_i=(u_i,v_i,w_i)$. The speeds of the particles are between $0$ ...
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1answer
1k views

Average kinetic energy of molecules hitting a surface

I am trying to prove that the average kinetic energy of gas molecules hitting a containers surface is $2k_{B}T$ instead of the average for the entire gas, which is $\frac{3}{2}k_{B}T$, where $k_{B}$ ...
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0answers
13 views

Phase space density function and Probability density function

I am reading a text which talks about the WIMP speed distribution in the galactic halo in the frame of the Sun and Earth. The point where I am stuck it is trying to explain the concept of ...
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1answer
42 views

Where is the difference to a quantum mechanic system with collapsing wavefunction in this experimental setup?

Let’s use a disc throwning system, where two porcelain plates are thrown at once and in different directions, one with its axis horizontal and the other vertical. To catch the plates we use a detector,...
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2answers
270 views

What's the relationship between probability amplitudes and amplitudes of a wave?

Amplitudes or probability amplitudes are the complex coefficients of the linear combination of states which represent other quantum physical states. The amplitude of a wave can be interpreted as a "...
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4answers
441 views

Is there a mathematical basis for Born rule?

Wave function determines complex amplitudes to possible measurement outcomes. The Born Rule states that the probability of obtaining some measurement outcome is equal to the square of the ...
60
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8answers
5k views

Why is the application of probability in QM fundamentally different from application of probability in other areas?

Why is the application of probability in quantum mechanics (QM) fundamentally different from its application in other areas? QM applies probability according to the same probability axioms as in other ...
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1answer
82 views

Bohr's Correspondence Principle and the Born Rule

Bohr's correspondence principle and the Born rule are related right? The correspondence principle states that the behavior of systems described by the theory of quantum mechanics reproduces classical ...
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1answer
287 views

Outcome of measuring $L_x$ of a linear combination of hydrogen states

I have encountered a question: What are the possible outcomes in measuring $L_{x}$ and what are the corresponding probability of the state: $\Psi(r,0)=1/2(\Psi_{200}+\Psi_{310}+\Psi_{311}+\Psi_{31-...
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1answer
48 views

Probability of finding a particle in a superposition

In QM, is it possible to ask what the probability of finding a particle in a superposition will be? Once a particle is in a superposition, it is possible to find out the probability that it will be ...
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24 views

Aerodynamics of a bed sheet

Given the mass of a bed sheet and its area, is there any way of determining the probability of it landing "perfectly" when it is jerked up on the bed (by jerk i mean when you are making your bed and ...
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1answer
58 views

What is Wave Function? [duplicate]

Well, what is the meaning of wave function? What does it represent? In Schrodinger's equation, we find the value of Ψ. But what is Ψ exactly? Max Born only gave an explanation of what $Ψ^2$ (the ...
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2answers
48 views

Using Boltzmann distribution, what is the ratio of probabilities of two states?

I got the probability of state $i$ (in terms of Boltzmann distribution) as $$p_{i}=\frac{1}{Z_{i}}e^{-\epsilon _{i}/{kT}},$$ where $Z_{i}$ is the canonical partition function: $$Z_{i}=\sum_{i}e^{-\...
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4answers
508 views

Why the self-information is $-\log(p(m))$?

Why is self-information given by $-\log(p(m))$? Shannon derived a measure of information content called the self-information or "surprisal" of a message $m$: $$I(m) = \log \left( \frac{1}{p(...
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2answers
97 views

What is the mathematical reasoning behind Schrodinger's equation preserving its normalization, with the evolution of time?

I am currently in high-school, currently working on a physics research on the normalization of the Schrodinger's equation. I was quite interested on how we can mathematically explain preservation of ...
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4answers
196 views

Does $j=\rho v$ hold in quantum mechanics?

Let's consider the current of probablity $\vec{J}(\vec{x},t)$ associated to a particle of mass $m$ with wave function $\psi(\vec{x},t)$, given by $$\vec{J}(\vec{x},t)=\frac{i\hbar}{2m}(\psi \nabla\...
2
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1answer
309 views

Optical theorem in QFT

I've been working with the Optical theorem in the case in which final and initial states are equals and I have the following doubt. Let's write the scattering matrix $S$ as: $$S = 1 + i·T \tag1$$ ...
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28 views

Negative probability distribution function for Dirac equation

People say that the probability density function of the continuity equation for the Dirac equation is definite positive. I wanted to see it myself and followed the same path as Bjorken & Drell's ...
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0answers
29 views

List of Replica Symmetry results for different models?

Does anyone know of a good source that might have a list of problems or models along with what kind of replica symmetry they are conjectured to have? I am aware of some of the more famous results, e....
0
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1answer
317 views

Lorentz distribution in emission peaks

Sometimes spectral peaks are fitted using a very pathological function named the Lorentz/Cauchy distribution. The Lorentz distribution has the property of not having a defined mean nor standard ...
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1answer
32 views

What parameters determine the probability of virtual photon emission/absorption?

Suppose an electron is producing an electric field by emission of virtual photons and interacting with other particles. What parameters determine the probability that it will emit at least one virtual ...
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26 views

Stochastic version of the Kirchoff circuit law

I assume this question could be written in a non-technical jargon, but I will try to be as simple as possible. The Kirchoff circuits law assert that the sum of inward and outward currents at a node ...
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0answers
96 views

Method to build a polyhedral die with given probabilities [closed]

Let's define a die as a polyhedron that, if rolled over a perfect horizontal plane, ends up being in a physically stable unambiguous state labelled $n$. The die has $N$ states. Each state $n$ has a ...
4
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1answer
7k views

In how many possible ways can a photon be emitted?

I am currently studying atomic physics, and I encountered the question above. I am posting this question because I can't afford to move on with even the tiniest bit of uncertainty in my understanding ...
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3answers
299 views

Is the probability current an observable?

Is the probability current in Quantum Mechanics an observable? If so, how can it me measured (directly or indirectly)?
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2answers
75 views

Some quantum-mechanical questions [closed]

I have recently started studying quantum mechanics, and here are some things that are really confusing me. Particle in a box: Supposedly, the square of the magnitude of the normalized wave function ...
6
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1answer
457 views

Is the Born rule indeed wrong?

This is a question about the validity of a preprint, arXiv:quant-ph/0509089, which claims that the "Copenhagen Interpretation of QM is incorrect" (same title, authored by Guang-Liang Li and Victor O.K....
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1answer
65 views

Interpretation of the wave function in newtonian spacetime

A Newtonian spacetime is a quintuple $(M, \mathcal{O}, \mathcal{A}, \nabla, t)$ where $(M, \mathcal{O}, \mathcal{A}, \nabla)$ is a 4 dimensional differentiable manifold with a torsion free connection, ...
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1answer
16 views

Do different liquids have different distributions of kinetic energy of their particles, and does this influence their vapor pressure significantly?

This is a bit of a cross-over between a physics and a chemistry question. When we say a liquid has temperature $T$ we make a statement about the mean kinetic energy of a particle in that liquid. That ...
2
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1answer
300 views

Cosmological fluctuations: what is gaussian?

When we are speaking about gaussianity and non-gaussianity in a cosmological context, what is gaussian or non-gaussian in the CMB? What would a non gaussian CMB look like compared to a gaussian one? ...
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1answer
50 views

Probability of successive measurements

Suppose I have states $|1\rangle$ and $|2\rangle$, and my system is in a quantum mixed state \begin{equation} c \left( |1\rangle + \sqrt{3} |2\rangle \right). \end{equation} In a first measurement I ...
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2answers
90 views

Relation between the propagator and probability for the infinite well

This may be an easy question, but I am really confused about it. For the infinite square well, the (time-dependent) energy eigenfunctions are (inside the well):$$\psi_n(x,t) = \sqrt{2/L}\:e^{-iE_nt/\...
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71 views

Is the “probabilistic nature of quantum mechanics” and quantum randomness the same?

Digital Physics are a branch of hypotheses about the fundamental physics of our universe. They basically describe the universe as an analogy to a computer and defend that everything in the universe is ...
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3answers
76 views

Measurement of a State Not in the Eigenbasis of the Operator

Suppose I have a two dimensional Hilbert space $\{ |0 \rangle,|1\rangle \}$ with these states being orthonormal. Now suppose I have the Hamiltonian $H=|1\rangle \langle 0|+|0\rangle \langle 1| .$ It ...
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2answers
143 views

Probability of a specific energy state

We consider the normalized wave function: $$\psi(x,t) = \sqrt{\frac{2}{3}}\psi_0(x)\exp\left(\frac{-iE_0t}{\hbar}\right) + \sqrt{\frac{1}{3}}\psi_1(x)\exp\left(\frac{-iE_1t}{\hbar}\right) $$ To ...
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1answer
118 views

X-ray diffraction analyisis: The angle of elastic x-ray scattering

What is the scattering angle distribution for x-rays (in the 8keV range) scattered elastically? I work with XRD analysis, which is fundamentally basede on these elastic scatterings of x-rays. I read ...
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1answer
49 views

Probability of finding hydrogen atom in its ground state given an initial state

So I came across this question that asked what is the probability of a hydrogen atom which is prepared in an initial state $\Psi (\vec{r},t)$ to be in the ground state $\psi_{100}(\vec{r}) =2exp(-r)Y_{...
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1answer
137 views

Questions on ergodicity

The "definition" of an ergodic system is that the average of its states in phase space is the same as its average over time. So I was thinking to myself Is a pendulum an ergodic system? In this case,...
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1answer
124 views

Probabilities with the Density Matrix

The density matrix of the system is given by: $$ [\rho_{S}(t)]_{mn} = [\rho_{S}(0)]_{mn} e^{-i\omega_{0}(m - n)t} e^{-i \delta(t)(m^2 - n^2) - \gamma(t)(m - n)^2}, ...
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39 views

Error in histogram measurements

I ran into the following statement here and here but I believe it's more general. Let's suppose we're running a simulation of a system and we are interested in the distribution of a quantity (say $M$...
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1answer
34 views

Lack of intuition for distribution function in micro and macro state description

I am a mathematician who is trying to understand statistical mechanics / thermodynamics. I need a hint wrt the interpretation / meaning of the distribution function. Currently I seem to have a basic ...
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1answer
59 views

How to evaluate the probability when a particle is detected?

Everyone knows the standard probability interpretation of the quantum mechanics. For example, the wave function of some particle at some time $t$ is $\psi (x,t)$. Therefore, if the particle is ...
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2answers
644 views

Probabilities in non-stationary states

I'm confusing myself. Let's represent some state in the eigenbasis for Hydrogen: $$|\psi\rangle = \sum_{n,l,m}|n,l,m\rangle\langle n,l,m|\psi\rangle.$$ Now denote the initial state by $\psi(t=0)\...
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1answer
32 views

Derive properties of fluids using Monte Carlo method on brownian motion

Given a particle inside a fluid, it's known that its movement will be unpredictable due to the random collisions with the particles of the fluid. However, the distance from the origin of motion will ...
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Converting a discrete statistical energy distribution to a continuous version

The probability of finding a particle at a particular energy level when energy is considered discrete is according to Boltzmann: $$P(E_j) = \frac{g_j\cdot e^{-\beta E_j}}{\sum_{j=1}^\infty g_j \cdot ...
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1answer
133 views

In statistical mechanics, why do we consider number of states of a system in energy interval?

In statistical mechanics,when we go for calculating the no. of accessible micro states of a system, I notice that we always calculate the no. of micro states of that system in some energy interval say ...
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27 views

Probability In a Nuclear Transmutation Question

How much cobalt will form into zinc when you add a mole of the set (3 protons, 3 electrons and 5 neutrons) to the cobalt? I cannot figure out how to find the probability of creating a certain ...
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2answers
892 views

How does gravity affect the wavefunction of a particle?

I'm wondering how gravity affects the wave function of a particle. For example, if we shot a particle horizontal to the earth at a vertical detector screen, would the distribution on the screen be ...
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1answer
48 views

What does conservation of probability mean in Classical Mechanics and why is it true?

In the context of the Liouville equation, regularly the conservation of probability is invoked. (Of course, the overall probability is always conserved but this is a truism and not what is meant here. ...