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3
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1answer
85 views

Detailed balance condition for coupled Langevin equation

Suppose $a$ and $m$ are real variables and they satisfy the following two coupled Langevin equations: $$ \dot{a}=F_a(a,m)+\eta_a(t);\quad\dot{m}=F_m(a,m)+\eta_m(t); $$ where $\eta_a$ and $\eta_m$ are ...
-3
votes
1answer
58 views

probability amplitude and path integrals [closed]

Recently, I have been learning about path integrals and I was wondering, can the probability of a certain path be weighted more in a path integral? Said in another way, can certain paths have more ...
0
votes
0answers
16 views

Canonical Ensemble (Probability)

In canonical ensemble, $$\rho_{normalized}=\frac{e^{-\beta H}}{Z}$$ where Z is a partition factor, now why $$dP(q_{i},p_{i})=\frac{\rho d^{3N}pd^{3N}q}{h^{3N}}$$
1
vote
2answers
112 views

Why is time evolution of wavefunctions non-trivial?

(Note: This post focuses on a single simple example, however I'm asking about the error in general in my logic). Consider the infinite potential well "particle in a box" system described by ...
0
votes
4answers
51 views

Question about interpreting probabilities in QM [duplicate]

For the example of an infinite square well, $\psi(x)=0$ for $x$ outside the well/interval, and we are to interpret this as the particle cannot be found outside the well because ...
1
vote
1answer
55 views

Probability distribution of phase-space reconstructions

I am unable to find resources regarding the probability density and distribution of non-linear chaotic systems in phase space. For example, if a discrete one-dimensional system, say the logistic ...
3
votes
3answers
521 views

Wavefunction, probability and impossible events

A friend of mine asked me a question, which I considered trivial at first, but after a while gave rise to some doubts. For instance, we have a potential well in 1 dimension defined by $$ V(x)= ...
1
vote
0answers
15 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 ...
0
votes
2answers
59 views

Expectation value expression Quantum Mechanics

Whilst working on a project I kept stumbeling across two different expressions for the standard deviation $\Delta{X}^2 = <(X - <X>)^2 >$ and the other $\Delta{X}^2 = <X^2> - ...
1
vote
2answers
77 views

Second Law from Statistics

Hi all I hope you can help me with the statistical origins of the Second Law. I cannot find anything that mathematically proves that order from disorder is impossible only improbable Leading me to ...
1
vote
0answers
14 views

Distribution and different ways of distribution

Is "the number of ways of of distributing $N$ things across a fixed set of energy levels the same as "the number of ways a particular distribution can be realised? My book seems to say that $W$ is ...
1
vote
2answers
45 views

Entropy-A question. [closed]

If I have 100 coins then a macrostate is how many heads/tails I have, a micro state is the facing of each individual coin of the 100, but what then is a "configuration" in this example? It is a basic ...
0
votes
0answers
68 views

Boltzmann distribution - statistical mechanics

I have just followed a derivation of the Boltzmann distribution which I have never seen before, and I must say it is really intuitive. However I have a question as to how we can think of the Boltzmann ...
1
vote
2answers
85 views

If the universe is spatially infinite, and if something (A) is possible, does that mean the thing (A) happens?

Assuming that the universe is spatially infinite, extending outwards in all directions without end, and is consistent with what we have thus far observed, and predict to find (and predict to be out ...
0
votes
3answers
75 views

Can you pre-determine the result of a coin toss?

The question is fairly simple. Consider the following parameters which are known to you: 1.) Mass of the coin 2.) The force applied on the coin 3.) The point where the force is applied on the coin ...
1
vote
0answers
38 views

Relaxation time approximation in Drude model apparant paradox

In the Drude model of the free electron gas to explain the conduction of a metal, the relaxation time approximation that the electron has a collision in an infinitesimal time interval $dt$ is ...
0
votes
0answers
35 views

Charge density within radius r from the nucleus

The probability of finding an electron within radius $r_b$ for Hydrogen near the center ($r_b<< a_0$) is approximately equal to zero (according to 1s orbital curve). Does this imply that the ...
4
votes
3answers
924 views

Why does Law of Large Numbers work?

Often I see books and professors reasoning that, in order to make a good experiment, many measurements are necessary because then the average value of a quantity is closer to the expected value ...
0
votes
1answer
51 views

How was phase randomly changing in CHSH test (M. A. Rowe and others)?

Measuring phase of photon should always be random while checking CHSH inequality, but i can't explain this: http://qudev.ethz.ch/content/courses/QSIT08/pdfs/Rowe01.pdf (the most clear experiment i ...
0
votes
1answer
104 views

If the universe is infinite, should there be a duplicate of me with probability 1? [duplicate]

I was just wondering: if the universe is really infinite, and there is a certain probability to find a life form just like me on another planet (for example $1.0 \cdot 10^{-150}$), is it therefore ...
1
vote
1answer
84 views

$\sigma$-additivity of Probability and Quantum Mechanics

$\sigma$-additivity - probability of a sum of countable number of pairly disjoint events equals a sum of probabilities of these events. (3. Axiom of Probability) For pairly disjoint sets $A_k$ ...
1
vote
0answers
27 views

Noise of a fiber optic gyro

I have not much experience with noise handling or calculations, furthermore in my researches couldn't find a similar problem, so here is my attempt: Having a fiber optic gyro that is rated with a ...
0
votes
1answer
33 views

To find the probability? [closed]

The mass of the earth is 5.975 X 10^27 g of average atomic weight 30.00 g. The fraction (by weight) of the earth that is gold has been estimated to be 3 X 10^-9. The atomic weight of gold is about ...
1
vote
0answers
16 views

Why can't we use the Neyman-Pearson likelihood ratio directly?

If you have a bunch of events and would like to choose a cut to distinguish background and signal, you can take the likelihood ratio $$ \lambda(\vec x) = \frac{f(\vec x| s)}{f(\vec x| b)} $$ and the ...
2
votes
1answer
62 views

Ising model on lattices with (vertical side length) $\neq$ (horizontal side length)

Consider the Ising model with nearest neighbours interactions on a rectangular lattice $L\times M$. If $L=M$ (2-dimensional square lattice), it is known (e.g. by Peierls argument or Onsager explicit ...
2
votes
0answers
87 views

Do doomsday arguments influence doomsday hypotheses?

The doomsday argument supposes that in the absence of any other knowledge, if we know the age of something now, we may assume that we are seeing it in the middle of its lifetime and then calculate our ...
4
votes
3answers
132 views

Why, in spin sums, we sum over final spin states and average over initial states?

I am reading Halzen's book about quarks and leptons and on page 120 he talks about spin sums. He says that in order to calculate the amplitude between unpolarized states we have to sum over FINAL ...
3
votes
2answers
134 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( ...
5
votes
1answer
116 views

Which position and momentum distributions arise from some wave function?

Consider a particle in one dimension with wave function $\psi(x)$. The probability density function describing how likely it is to find it in a given position is given by ...
0
votes
0answers
64 views

Definition of transmission and reflection probability

This is a basic question, but it does not seem to be well defined anywhere. Generally, two terms are mixed somewhat randomly: transmission PROBABILITY and transmission coefficient. So to be clear, ...
0
votes
1answer
40 views

Probability to be in a particular state

If I have a wavefunction $\psi = \sum_{n=0}^{\infty} a_n e^{i \phi_n} | n \rangle$ and $(|n \rangle)$ is a set of orthonormal functions. Is it correct that the probability to be in a state $|k\rangle ...
2
votes
1answer
125 views

Was Max Born the first to notice a connection between quantum mechanics and randomness?

Max Born introduced the Born Rule in a paper from 1926. But was this really the first time that a connection between quantum mechanics and randomness was noticed? Today, quantum mechanics and ...
1
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0answers
33 views

Books on collision probability and collision processes

Are there any books specifically on collision processes between atoms and molecules and collision probability? I would like to get an overview of the factors that determine collision probability ...
0
votes
0answers
60 views

probability of sequence for given rate constants

lets consider a copolymer, $C_{r,s}^A$ containing r number of A monomers and s number of B monomers with A at the reactive end of the polymer. The equilibrium constant for A-A, A-B, B-A, and B-B bonds ...
0
votes
3answers
65 views

Probability and lifetime

What is the relation between the lifetime of a particle and the probability of decaying that particle? Here it says that the probability of survival is exponential if the decay process is a Poisson ...
6
votes
5answers
868 views

Differences between probability density and expectation value of position

The expression $\int | \Psi\left(x\right)|^2dx$ gives the probability of finding a particle at a given position. If wave function gives the probabilities of positions, why do we calculate ...
2
votes
2answers
180 views

Differences between wave function and set of orthonormal wave functions?

I'm reading a QM book. It first says for wave function: "The state of a physical system (or particle) is completely specified by an entity associated with it called a wave function, Ψ , that in ...
3
votes
5answers
288 views

About the definition of expectation value in quantum mechanics

In quantum mechanics, the expectation value of a observable $A$ is defined as $$\int\Psi^*\hat A\Psi$$ But in probability theory the expectation is a property of a random variable, with respect to a ...
4
votes
0answers
57 views

Help with deriving an asymptotic expression

Note: I don't know if this is the best place for this question, because it is very specific. However, I'm not sure of a better place to go (apart from one of the other SE's). If you have a ...
0
votes
1answer
36 views

How many state configurations are possible for $N$ particles in completely different states?

How many state configurations are possible for $N$ particles in completely different states? I cannot remember if the total number of state configurations for $N$ particles in completely different ...
2
votes
1answer
254 views

Proof of Liouville's theorem: Relation between phase space volume and probability distribution function

I understand the proof of Liouville's theorem to the point where we conclude that Hamiltonian flow in phase-space is volume preserving as we flow in the phase space. Meaning the total derivative of ...
-1
votes
3answers
911 views

Differences between wavefunction, probability and probability density?

I am trying to understand the differences between wavefunction, probability and probability density. There are different definitions on the internet. For example: ...
1
vote
1answer
35 views

Why does the probability of obtaining a value of a measurement follow from Dirac's general assumption?

In Dirac's The Principle of Quantum Mechanics he makes the general assumption that "if the measurement of the observable $\xi$ for the system in the state corresponding to $|x\rangle$ is made a large ...
0
votes
0answers
24 views

Mathematical calculation of probability of existence of planet similar to earth [duplicate]

Having a layman level of logic about probability ( read about it 10 years ago, so pardon if it's still not right completely) what i know that the calculation requires some knowledge about the number ...
1
vote
0answers
65 views

Probability and the propagator

Due to the Wiki article, "...In quantum mechanics and quantum field theory, the propagator gives the probability amplitude for a particle to travel from one place to another in a given time, or to ...
2
votes
1answer
117 views

From where randomness comes from and why it exists? [closed]

I recently began to study statistics and probability and I have two questions: Where does randomness come from? What is the source of randomness? Why does the randomness exist? Is it possible to ...
0
votes
0answers
68 views

Quantum mechanics and probability

I've done an intro course on QM and I'm now hoping to understand exactly how to use probability theory rigorously in solving problems. My question is: How do I do the same thing, or the closest thing ...
0
votes
2answers
46 views

Modeling Quantum Aspects with Probability

This is a question I've had a while about quantum theory. Many times when I look at books and equations about this subject matter I see that the use many concepts in probability. (Correct me if Im ...
0
votes
0answers
28 views

Stochastic process corresponding to Schrödinger evolution

In probability theory, the Fokker-Planck equations governs the trajectory of a sample path of a stochastic process -- say the heat equation in the case of a Wiener process. Consider a Gaussian ...
3
votes
1answer
84 views

How does determinism manifest out of QFT?

Classical electrodynamics is deterministic. QED is indeterministic, or probabilistically random. Yet they agree with each other? What am I missing?