The probability tag has no wiki summary.
2
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0answers
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Normalizing a continuous distribution [migrated]
I work at a help/tutoring center at my university. Today a kid came in with this problem. I've only studied math and haven't drifted into physics, but he had this problem:
Let ...
4
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3answers
261 views
+100
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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-1
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0answers
32 views
Possible outcomes of measurement on a state
I having some trouble understand a question I'm handed. I doesn't seem to be difficult, I think, but I'm having some trouble understanding what I actually have to do.
I have the following variable ...
2
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1answer
36 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 ...
0
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1answer
253 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 ...
1
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2answers
62 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
41 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
61 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
41 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
43 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 ...
7
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2answers
90 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. ...
1
vote
1answer
188 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, ...
2
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1answer
49 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
75 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 ...
-1
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0answers
18 views
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 ...
5
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4answers
2k views
Infinite universe - Jumping to pointless conclusions
I watched an episode of thee BBC Horizon series titled 'To infinity and beyond'.
In this program a number of respected physicists and mathematicians were talking about the nature of infinity and an ...
2
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5answers
1k views
Is it true that quantum mechanics technically allows anything to happen?
Maybe this is a silly question (I think it is), but it's a question I'm arguing with some of my friends for a long time.
The ultimate question is: Is everything (in our Universe) possible ?
I've ...
4
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2answers
88 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 ...
3
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2answers
47 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 $x=a\sin(\omega t)$. ...
0
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1answer
1k views
Would one actually find their doppleganger in a “Googolplex Universe”?
Related: Infinite universe - Jumping to pointless conclusions
I've recently become a fan of Numberphile, and today I happened to watch their video regarding Googol and Googolplex. In the video, ...
3
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3answers
141 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 ...
0
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1answer
395 views
Plotting Hydrogen's $2P_{x,y,z}$ Probability Densities in MATLAB [closed]
I have spent an unreasonable amount of time trying to plot $F(r,\theta,\phi)$ plane slices in MATLAB. I want to look at $x-y,y-z,x-z$ planes. Here's the function, specifically:
...
0
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1answer
89 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.
0
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0answers
23 views
Probability in Radiation Physics for electrons [closed]
The total linear attenuation coefficient for 10-keV electrons in water is 77.6 ÎĽm^-1, partitioned as follows:
Elastic scattering 38.2 ÎĽm^-1
Ionization 37.4
...
4
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6answers
498 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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vote
3answers
179 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
votes
1answer
365 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, ...
6
votes
1answer
43 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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1answer
143 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?
2
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2answers
149 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
...
0
votes
0answers
48 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
185 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
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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 ...
0
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3answers
242 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\\$$
...
2
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3answers
184 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 ...
4
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2answers
338 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 ...
1
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0answers
181 views
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 ...
13
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1answer
112 views
Monte Carlo integration over space of quantum states
I am currently facing the problem of calculating integrals that take the general form
$\int_{R} P(\sigma)d\sigma$
where $P(\sigma)$ is a probability density over the space of mixed quantum states, ...
2
votes
3answers
261 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 ...
4
votes
1answer
37 views
Convexity — reference request
I've been reading a few papers on generalized probabilistic theories, and have been struggling through proofs of some results that involve use of convexity and group theory, e.g. this paper on bit ...
6
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1answer
42 views
Allowed states vis-a-vis allowed dynamics in generalized probabilistic theories (GPTs)
In his work on information processing in GPTs http://arxiv.org/abs/quant-ph/0508211 Barrett speculates that the trade-off between allowed states and the allowed dynamics in a GPT is optimal in quantum ...
12
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2answers
94 views
Random Walk Randomly Reflected
Hi I am not specialist in probability so I will not be surprised if the answer for this question is just a simple consequence of well known results from the random walk theory.
In this case, I will ...
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2answers
46 views
Bell polytopes with nontrivial symmetries
Take $N$ parties, each of which receives an input $s_i \in {1, \dots, m_i}$ and produces an output $r_i \in {1, \dots, v_i}$, possibly in a nondeterministic manner. We are interested in joint ...
1
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1answer
166 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?
8
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1answer
451 views
The measure problem in the anthropic principle
The anthropic principle is based upon Bayesian reasoning applied to the ensemble of universes, or parts thereof, conditioned upon the existence of conscious observers. That still leaves us with the ...
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2answers
129 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
87 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). ...
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11answers
885 views
Negative probabilities in quantum physics
Negative probabilities are naturally found in the Wigner function (both the original one and its discrete variants), the Klein paradox (where it is an artifact of using a one-particle theory) and the ...
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0answers
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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 ...
20
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5answers
81 views
Connections and applications of SLE in physics
In probability theory, the Schramm–Loewner evolution, also known as stochastic Loewner evolution or SLE, is a conformally invariant stochastic process. It is a family of random planar curves that are ...
