The probability tag has no wiki summary.
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The Convolution of Two Probability Distributions [migrated]
The question asks for the convolution of two probability distributions f(x) and g(y), and the equation
$$C(x)=\int_{-\infty}^{\infty}f(x-t)g(t)dt$$
is given. I am given two probability distributions ...
0
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1answer
59 views
Quantum mechanics potential barrier problem
As going through my quantum mechanics I cam across a very interesting situation.Going through a potential barrier,if the particle has an energy $E$ less than $V_0$, $V_0$ is the potential barrier,it ...
2
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1answer
39 views
Probability density of detection of collinearly emitted photons in two detectors
Update:
As proposed by @dmckee, I added equation numbers and improved the display of some equations.
The answer by @Trimok inspired me to look at coordinate systems which are not specific to the ...
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0answers
24 views
Are negativity of the Wigner function and quantum behaviour equivalent?
I've read the following question: Negative probabilities in quantum physics
and I'm not sure I understand all the details about my actual question. I think mine is more direct.
It is known that the ...
1
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2answers
74 views
Probabilities in statistical mechanics
I am reviewing some concepts in statistical mechanics and am becoming confused with how to calculate probabilities when a system has $N$ non-interacting particles.
For instance, let's say we have ...
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0answers
43 views
The meaning of $p_{i}$ and $\rho^{i}$ as probabilities and densities in Quantum Mechanics
The question I have concerns the actual meanings of $p_{i}$ and $\rho^{i}$ Now $p_{i}:Meas_{I} \times D(H) \rightarrow [0,1]$, so for a particular set of Measurement matrices M and Density matrices ...
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0answers
119 views
Fermi's golden rule and Probabilities in QM
In Fermi's golden rule
$$P_{ab}(t)=2\pi t/\hbar \left|\langle\psi_b|V|\psi_a\rangle\right|^2 \delta(E_f-E_i)$$
for transition probability from state $a$ to $b$, how can the probability grow with ...
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3answers
354 views
Born's Rule, What is the Reason?
As far as I've read online, there isn't a good explanation for Born's Rule. Is this the case? Why does taking the square of the wave function give you the Probability? Naturally it removes negatives ...
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2answers
118 views
What is the probability density function over time for a 1-D random walk on a line with boundaries?
If a single particle sits on an infinite line and undergoes a 1-D random walk, the probability density of its spatio-temporal evolution is captured by a 1-D gaussian distribution.
\begin{align}
...
4
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3answers
128 views
Is there a phenomenon where physicists are only interested in the standard deviation of the quantity to be measured?
or a phenomenon where we can only measure the standard deviation ($\sigma_w$) of a variable $w$ and not the mean $\overline{w}$
4
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2answers
242 views
Why is quantum mechanics based on probability theory? [duplicate]
What makes us formulate quantum mechanics based on probability theory?
Isn't the real quantum world based on unknown laws to us?
Is it possible that results of an experiment will be measurable in ...
-1
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1answer
101 views
What is probability to find electron at certain distance from nucleus
Given for example, Hydrogen electron in ground state. What is probability to find that electron at certain distance (not interval of distances) from center of nucleus, for example at radial coordinate ...
2
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1answer
112 views
Probability for harmonic oscillator outside the classical region
I'm having some trouble finding an expression for the probability to find the particle outside the classical area in the harmonic oscillator.
I have a wavefunction defined as:
$\psi \left( x,\,t ...
1
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2answers
141 views
Classical/Quantum Coin Toss
I am having a brainfreeze moment and have confused myself, help appreciated!
Classical Coin: Heads OR tails.
Quantum Coin: Superposition Heads AND Tails.
Classical Mechanics: Deterministic (in ...
0
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1answer
90 views
spontaneous disintegration of an unstable particle
Suppose one wants to describe an unstable particle that spontaneously disintegrates with a life time say "tau". In that case the total probability of finding the particle is not constant. But should ...
0
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1answer
132 views
Physical interpretation of normalization of wave fuctions
Does normalization of wave function mean that we are getting our state vector to unit length? If that's the case what does it mean physically? Also is the underlying vector space finite dimensional? ...
1
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1answer
111 views
Fermi-Dirac Statistics
In Fermi-Dirac statistics the probability of being in a certain energy state is
$f(E) = [1 + \exp(\frac{E-E_F}{k T})]^{-1}$
In the area that I'm looking at the texts always assume the population's ...
0
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1answer
54 views
Is this hypo-theoretical model of future prediction feasible? [closed]
First let me state that I am not, nor ever have I been, a physics student. I am working on an idea for a book I'm writing.
This is a thought experiment that posits the existence of a computer system ...
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2answers
108 views
How to design a deliberately biased coin?
For demonstrating basic probability concepts, it would be nice to have a coin-like object that lands heads/tails not in 50/50% ratio, but biased in a way that can be revealed in a short experiment. ...
4
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2answers
108 views
How do you come up with a POVM?
This is a made-up example, just to understand a concept. If changing the probability values aids your explanation, that's fine by me.
Say you have a physical quantity $E$ that can take values 1, 2, 3 ...
2
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1answer
61 views
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?
$\mathbb{E}[C^2] = a^2 + 2a\mathbb{E}[B] + \mathbb{E}[B^2]$
...
4
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2answers
93 views
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
64 views
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 $x=a\sin(\omega t)$. ...
6
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3answers
405 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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3answers
160 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
99 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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6answers
953 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
302 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.
$$\langle x \rangle = \int\limits_{-\infty}^\infty |\Psi|^2 x \, ...
5
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1answer
433 views
't Hooft for laypersons
I have looked at some of 't Hooft's recent papers and, unfortunately, they are well beyond my current level of comprehension. The same holds for the discussions that took place on this website. (See, ...
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0answers
49 views
Classical analogy of particle decay
Is there some classical system that mimics the decay law for particles $N(t)=N(0)e^{-(Q_1+Q_2..)t}$ with multiple decay modes? To help me visualize this process. Something like a barrel of water with ...
6
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3answers
199 views
Is “entanglement” unique to quantum systems?
My text shows (sections 0.2 and 0.3) that the joint "state space" of a system composed of two subsystems with $k$ and $l$ "bits of information", respectively, requires $kl$ bits to fully describe it. ...
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0answers
57 views
Equivalence of simple formulations of qubit entanglement
I'm reading some very elementary treatments of quantum computation and am unsure about the correspondence among "definitions" of qubit entanglement.
One definition states that (1) the bits of a ...
4
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3answers
252 views
Could quantum mechanics work without the Born rule?
Slightly inspired by this question about the historical origins of the Born rule, I wondered whether quantum mechanics could still work without the Born rule. I realize it's one of the most ...
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3answers
308 views
Normalisation factor $\psi_0$ for wave function $\psi = \psi_0 \sin(kx-\omega t)$
I know that if I integrate probabilitlity $|\psi|^2$ over a whole volume $V$ I am supposed to get 1. This equation describes this.
$$\int \limits^{}_{V} \left|\psi \right|^2 \, \textrm{d} V = 1\\$$
...
6
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2answers
395 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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0answers
203 views
Probability and probability amplitude [duplicate]
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 ...
2
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2answers
162 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
...
3
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3answers
281 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
52 views
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 ...
2
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2answers
203 views
Are probability-preserving variations of QT with respect to the Born rule mathematically possible?
Is it possible to create (m)any theoretically workable framework(s) - that do(es) produce probabilities - by taking QM and replacing the Born(-like) rule(s) with something that is not equivalent to it ...
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1answer
194 views
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?
2
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2answers
139 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
96 views
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). ...
3
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0answers
146 views
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 ...
4
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1answer
158 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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5answers
380 views
Born rule and unitary evolution
Is the Born rule a fundamental postulate of quantum mechanics, or can it be inferred from unitary evolution?
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0answers
60 views
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
277 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 ...
2
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4answers
388 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
84 views
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 ...
