The probability tag has no wiki summary.
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Probability distributions [migrated]
What is the probability that a random number [0,1) will lie in [0.5,0.6]?
As far as I know, there are 3 probability distributions in physics we usually use, but I am not sure when we can use ...
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1answer
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Statistical sum of physical quantities in a quantum system
Let $C = A + B$ (statistical sum, so $\mathbb{E}[C] = \mathbb{E}[A] + \mathbb{E}[B]$), and let $p(A = a) = 1$. Are the following true?
$\mathbb{E}[C^2] = a^2 + 2a\mathbb{E}[B] + \mathbb{E}[B^2]$
...
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Independent systems and Lagrangians
Definition 1:
The notion of independent systems has a precise meaning in probabilities. It states that the (joint) probability or finding the system ($S_1S_2$) in the configuration ($C_1C_2$) is ...
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2answers
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Probability of position in linear shm?
The problem that got me thinking goes like this:-
Find $dp/dx$ where $p$ is the probability of finding a body at a random instant of time undergoing linear shm according to $x=a\sin(\omega t)$. ...
3
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2answers
148 views
Determinism, classical probabilities, and/or quantum mechanics?
[I]f you want a universe with certain very generic properties, you seem forced to one of three choices: (1) determinism, (2) classical probabilities, or (3) quantum mechanics. [My emphasis.]
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Rolling a perfect square [closed]
If a 20-sided fair die with sides distinctly numbered 1 through 20 is rolled, the probability that the answer is a perfect square can be expressed as a b where a and b are coprime positive ...
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3answers
137 views
Does entropy alter the probability of independent events?
So I have taken an introductory level quantum physics and am currently taking an introductory level probability class. Then this simple scenario came up:
Given a fair coin that has been tossed 100 ...
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1answer
86 views
Probabilistic vs Statistical interpretation of Double Slit experiment
Why is it assumed that the results seen in the double slit experiment are probabilistic and not just a statistical result of some unknown variable or set of variables within the system.
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Probability in Radiation Physics for electrons [closed]
The total linear attenuation coefficient for 10-keV electrons in water is 77.6 μm^-1, partitioned as follows:
Elastic scattering 38.2 μm^-1
Ionization 37.4
...
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6answers
372 views
Probability amplitude in Layman's Terms
I am basically a Computer Programmer, but Physics has always fascinated and often baffled me.
I have tried to understand probability density in Quantum Mechanics for many many years. What I ...
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3answers
146 views
Operators explaination and momentum operator in QM
I know and understand why equation below holds. But i am new to operator thing in QM and would need some explaination on this.
$$\langle x \rangle = \int\limits_{-\infty}^\infty |\Psi|^2 x \, ...
6
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1answer
358 views
't Hooft for laypersons
I have looked at some of 't Hooft's recent papers and, unfortunately, they are well beyond my current level of comprehension. The same holds for the discussions that took place on this website. (See, ...
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47 views
Classical analogy of particle decay
Is there some classical system that mimics the decay law for particles $N(t)=N(0)e^{-(Q_1+Q_2..)t}$ with multiple decay modes? To help me visualize this process. Something like a barrel of water with ...
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3answers
183 views
Is “entanglement” unique to quantum systems?
My text shows (sections 0.2 and 0.3) that the joint "state space" of a system composed of two subsystems with $k$ and $l$ "bits of information", respectively, requires $kl$ bits to fully describe it. ...
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0answers
54 views
Equivalence of simple formulations of qubit entanglement
I'm reading some very elementary treatments of quantum computation and am unsure about the correspondence among "definitions" of qubit entanglement.
One definition states that (1) the bits of a ...
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3answers
169 views
Could quantum mechanics work without the Born rule?
Slightly inspired by this question about the historical origins of the Born rule, I wondered whether quantum mechanics could still work without the Born rule. I realize it's one of the most ...
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3answers
219 views
Normalisation factor $\psi_0$ for wave function $\psi = \psi_0 \sin(kx-\omega t)$
I know that if I integrate probabilitlity $|\psi|^2$ over a whole volume $V$ I am supposed to get 1. This equation describes this.
$$\int \limits^{}_{V} \left|\psi \right|^2 \, \textrm{d} V = 1\\$$
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2answers
322 views
Amplitude of Probability amplitude. Which one is it?
QM begins with a Born's rule which states that probability $P$ is equal to a modulus square of probability amplitude $\psi$:
$$P = \left|\psi\right|^2.$$
If I write down a wave function like this ...
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Probability and probability amplitude
What made scientists believe that we should calculate probability $P$ as the $P = \left|\psi\right|^2$ in quantum mechanics? Was it the double slit experiment? How? Is there anywhere in the ...
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2answers
148 views
Why does the amplitude of a ripple tells us that it is a particle?
The quote below is from Matt Strassler's blog:
a particle is a ripple with many crests and troughs; its amplitude,
relative to its overall length, is what tells you that it is a single
...
2
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3answers
255 views
Probability and probability amplitude
The equation:
$$P = |A|^2$$
appears in many books and lectures, where $P$ is a "probability" and $A$ is an "amplitude" or "probability amplitude". What led physicists to believe that the square of ...
6
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1answer
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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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1answer
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Parallel universe and Infinite monkey theorem [closed]
Is the Infinite monkey theorem helpful for determining the existence of the very same our universe somewhere else?
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2answers
124 views
Computing microstate probabilities based on Boltzmann distribution for chemical systems - Is it rigorous?
One approach to predicting the folded structure of a polymer (DNA, RNA, protein) is to compute the probability that any particular part of the polymer $x_i$ is "paired" with another part of the ...
2
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1answer
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Basic question about probability and measurements
Say I have a Galton box, i.e. a ball dropping on a row of solid bodies. Now I want to calculate the probability distribution of the movement of the ball based on the properties of the body (case A). ...
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Electron hopping among molecules - Marcus equation
I'm running out of professors to talk to, and I need to clarify a couple of things for the sake of making a realistic model of electron travel through a mesh.
This is about calculations of electron ...
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1answer
212 views
Expressions for canonical partition function and probabilities $p(E_i)$
Given an atom with 4 allowed states corresponding to the energy levels
$E_1 = 0$, $E_2 = E$, and $E_3 = 2E$ with degeneracies 1, 1, and 2 respectively.
How do I find the expressions for the ...
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1answer
125 views
Probability in Quantum Mechanics
Do you need to take a probability/statistics course for Quantum Mechanics, or is the probability in quantum mechanics so rudimentary that you can just learn it along the way? I'm in doubt as to ...
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0answers
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How to explain Tsirelson's inequality using extended probabilities?
How to explain Tsirelson's inequality using extended probabilities?
Some people have tried explaining the Bell inequalities using extended probabilities.
For instance, a pair of entangled photons ...
3
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2answers
211 views
What is the physical interpretation of the density matrix in a double continuous basis $|\alpha\rangle$, $|\beta\rangle$?
(a) Any textbook gives the interpretation of the density matrix in a single continuous basis $|\alpha\rangle$:
The diagonal elements $\rho(\alpha, \alpha) = \langle \alpha |\hat{\rho}| \alpha ...
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4answers
303 views
If wave packets spread, why don't objects disappear?
If you have an electron moving in empty space, it will be represented by a wave packet. But packets can spread over time, that is, their width increases, with it's uncertainty in position increasing. ...
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1answer
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How to solve the tranmission probability in an evolution of a quantum system
I've just learned the evolution of some quantum system for about a week, and our homework sometimes something like this. I don't quite have any idea of solving this kind of problem.
Can you help ...
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1answer
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Boundary conditions from single-valuedness of spherical wavefunctions
This question is a follow-up to David Bar Moshe's answer to my earlier question on the Aharanov-Bohm effect and flux-quantization. What I forgot was that it is not the wavefunction that must be ...
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0answers
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Modeling the probability of a photodiode measuring photons targets at a neighbor
In current digital cameras, sensors are arrays of photodiodes which "transform" photons energy to electrons. I am aware that the probability of a photon to generate an electron is modeled by a Poisson ...
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1answer
180 views
Simulating quantum network of harmonic oscillators
Let's say that I have a system of $n$ particles $p_1,\ldots,p_n\in\mathbb{R}^3$ (where $n$ here is on the order of 10,000). Furthermore, suppose we have a graph $G=(V,E)$ describing some network, ...
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2answers
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Probability wave speed of dispersion and interference
I'm a layperson learning about quantum mechanics and probability waves. My understanding is that the probability wave for the position of a particle disperses throughout all of the universe.
I have ...
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1answer
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How to determine the probabilities for a cuboid die?
Imagine we take a cuboid with sides $a, b$ and $c$ and throw it like a usual die. Is there a way to determine the probabilities of the different outcomes $P_{ab}, P_{bc}$ and $P_{ac}$? With $ab$, ...
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3answers
265 views
Propagators and Probabilities in the Heisenberg Picture
I'm trying to understand why
$$\Bigl|\langle0|\phi(x)\phi(y)|0\rangle\Bigr|^2$$
is the probability for a particle created at $y$ to propagate to $x$ where $\phi$ is the Klein-Gordon field. What's ...
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1answer
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How to interpret a negative failure rate?
In statistical engineering the "hazard rate" of a distribution is defined as:
$$r(x)=\frac{f(x)}{1-F(x)}$$
where $f(x)$ and $F(x)$ are the PDF and CDF. Basically $r(x)$ is the odds that, having ...
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2answers
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Diffusion of probability amplitudes
Let's say I have a probability amplitude $\psi:\Sigma\rightarrow\mathbb{C}$ for some domain $\Sigma$ (so, $\psi$ satisfies $\int_\Sigma |\psi|^2=1$). Is there a way to use $\psi$ as initial ...
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2answers
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Similarity of probability amplitude functions
Let's say I have two probability amplitude functions given by $\psi_1$ and $\psi_2$. That is, $\psi_i:\Sigma\rightarrow\mathbb{C}$ for some domain $\Sigma$ with $\int_\Sigma|\psi_i|^2=1$ for ...
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231 views
Mathematical probabilistic interepretation of probability amplitude
As a warning, I come from an "applied math" background with next to no knowledge of physics. That said, here's my question:
I'm looking at the possibility of using probability amplitude functions to ...
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4answers
244 views
Are probabilities really tangible physical real numbers?
Probabilities are usually considered to be a real number between 0 and 1. A real number has an infinite decimal expansion. Are probabilities really real numbers? Is the infinite decimal expansion ...
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2answers
460 views
How do I figure out the probability of finding a particle between two barriers?
Given a delta function $\alpha\delta(x+a)$ and an infinite energy potential barrier at $[0,\infty)$, calculate the scattered state, calculate the probability of reflection as a function of ...
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1answer
130 views
Probability using Klein-Gordon Equation
I read somewhere that the Klein-Gordon equation doesn't allow for conservation of probability. Can someone prove this mathematically?
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1answer
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Probability, quantum physics, and why (can't it/does it) apply to macroscale events?
Quantum physics dictates that there are probabilities that determine the outcome of an event, ie: the probability of a quark passing through a wall is X, due to the size of the quark in comparison to ...
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2answers
159 views
Average Neighbouring Impurity Separation in a Random 1D chain [closed]
I have a finite and discrete 1D chain (edit: linear chain, i.e. a straight line) of atoms, with unit separation, with a set number of impurities randomly distributed in the place of these atoms in ...
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3answers
281 views
Probability vs. degree of belief in facts of nature (“Plausibility”)
I just came across a line in a paper:
"Assume the probability that a Lagrangian parameter lies between $a$ and $a + da$ is $dP(a) = $ [...]."
This reminded me again of my single biggest qualm I have ...
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1answer
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Computing an average escape distance for a particle
Somewhere in a two dimensional convex bulk of particles (pic related) on a random position a reaction takes place and a particle is sent out in a random direction with a constant velocity $v$.
What ...
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2answers
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What is the minimal set of expectation values I need in a statistical model?
At least if $\vec v$ is really only a one dimensional parameter, measuring all the moments $\langle v^n \rangle_f$ seems to give me all the information to compute $\langle A \rangle_f$ with $A(v)$ ...
