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2
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0answers
58 views

Quantum Mechanics and Economics… What

I was reading this paper: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2002698&download=yes The author has the model presented here: ...
1
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1answer
67 views

Why is probabilty conserved under time evolution of a system in quantum mechanics?

I've studied quantum mechanics to a certain degree, but one question that I've never been able to get a fully satisfactory answer to is why probability is conserved (by this I mean that it has either ...
1
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2answers
170 views

Number of microstates compatible with two boxes

From my notes I have: From one point of view there are many more microstates compatible with the LHS than the RHS, in fact the relation between the number of microstates is ...
0
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2answers
114 views

Why do termite pellets fall in a perfect circle?

I was just wondering why termite pellets fall down from my bed in a perfect circle. You can see from the images that the follow down on the floor making a perfect geometric figure which is void in ...
3
votes
1answer
62 views

Probability of photon emission

If a photon of a given wavelength is absorbed by an electron (for simplicity, let's assume the electron has only one excited state), does the probability that the electron jumps to its excited state ...
1
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0answers
43 views

Applicability of perturbation theory

Consider some system in some initial state $|k^{(0)}\rangle$. The probability that such a state makes a transition to some other state $|m^{(0)}\rangle$ can be computed to various orders in time ...
2
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1answer
59 views

Probability current in scattering problems

This is a section from Wikipedia: In regions where a step potential or potential barrier occurs, the probability current is related to the transmission and reflection coefficients, respectively ...
1
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1answer
64 views

Generalizing a Gaussian distribution

Perhaps this a nonsensical question but hear me out. I have a random variable $x$ whose moments I can calculate. The first moment $<x>$ is zero and the second $<x^2> = X^2$ is something ...
0
votes
1answer
46 views

Distinguishing between prepared and unprepared states Stern-Gerlach experiment

$ \newcommand{\bra}[1]{\left\langle #1 \right|} \newcommand{\ket}[1]{\left| #1 \right\rangle} \newcommand{\braket}[2]{\left\langle #1 \middle| #2 \right\rangle}$I have a problem and am confused as to ...
0
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1answer
35 views

Reference about probability to study statistical mechanics

I've started studying statistical mechanics but I feel that I need to understand probability better. There are tons of books on probabilities out there, but some of them just talk too much, with tons ...
-1
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2answers
37 views

Quantum measurement problem with eigenvectors (Dirac notation) [closed]

Ok so I've got two state vectors related to two other state vectors. $$|\alpha_1\rangle= (1/5)(3|\gamma_1\rangle+4|\gamma_2\rangle)$$ $$|\alpha_2\rangle= (1/5)(4|\gamma_1\rangle-3|\gamma_2\rangle)$$ ...
2
votes
2answers
89 views

Heisenberg uncertainty and probabilistic nature of QM

I am trying to understand whether the HUP and the probabilistic nature of QM are orthogonal or not. By that I mean that the HUP fundamentally derives from operators not commuting, which is the ...
0
votes
2answers
60 views

Probability from classical physics compared with quantum mechanics [closed]

$|\psi\rangle$=$\frac{1}{\sqrt5}|\uparrow_z\rangle+\frac{2}{\sqrt5}|\downarrow_z\rangle$ a)What is the probability of obtaining $+\frac{\hbar}{2}$ for $S_x$? b)If after obtaining ...
0
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2answers
87 views

Normalization of wave function meaning…?

I just have one question. I'm doing a problem where I'm told to normalize a wave function, which is split up into two regions, namely where $r \leq r_0$ and $r > r_0$. My question is, why am I ...
0
votes
1answer
40 views

Probability flux: spatial variation of the phase equal to momentum?

We can write any wave function as $$\psi(\vec x, t) = \sqrt{\rho(\vec x,t)}\exp{\left[\frac{iS(\vec x,t)}{\hbar}\right]}$$ for $S$ real and $\rho >0$. Here we interpret $\rho$ as the probability ...
3
votes
0answers
84 views

What can I expect to see in a oscillator exhibiting bifurcation?

I have a program which aims to simulate a Josephson Bifurcation Amplifier. I am currently trying to obtain a plot of the probability of bifurcation as a function of the ratio between the driving and ...
0
votes
5answers
306 views

Why do we need a wave function?

Assuming our only aim is to solve double slit experiment (or other problems that can be mapped into that). Knowing that electron does some strange thing not expected of a particle, we need a function ...
2
votes
2answers
109 views

How do probabilities emerge in the many-worlds interpretation?

My understanding is that at each quantized unit of time that a split occurs, every possible recombination of particles occurs in the 'objective' universe. If this is the case, what relevance to ...
0
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2answers
70 views

Can someone clarify which (if any) of these three QM assumptions is wrong?

I am trying to learn more about quantum mechanics. I am reading a book by Griffiths that I like. I'm trying to summarize what I've learned. So below I provided three assumptions. I'd like to know if ...
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0answers
28 views

On the probability of the existence of a similar observable universe

Let's assume a standard ($\Lambda$CDM + some simple inflation model) cosmology in an infinite universe. Really it doesn't matter much what cosmology we take, just that we're considering an infinite ...
0
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1answer
42 views

Thermodynamics vs Kinetics

As a chemical reaction approaches equilibrium, one of forward or backward reactions dominate the other. According to thermodynamics, this is because the gibbs free energy change for one is negative. ...
0
votes
1answer
50 views

Entropy and Gibbs Free Energy

I've been struggling with the notion of entropy and gibbs free energy for almost three days now. Different sources on and off the internet say different things about entropy. Gibbs Free Energy is ...
5
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4answers
603 views

What is the difference between + and - signs in superpositions of quantum states?

What is the difference between states $$ \frac1{\sqrt{2}} |11\rangle+\frac1{\sqrt{2}} |00\rangle $$ and $$ \frac1{\sqrt{2}} |11\rangle- \frac1{\sqrt{2}} |00\rangle~? $$ They will all eventually ...
0
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0answers
64 views

What is negative probability? [duplicate]

I am going through Quantum Computing, and thought to clear the basics first. So, I read blogs on Quantum Mechanics. They mention about Negative Probability. Now, what is that, this is very new to me. ...
0
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0answers
13 views

Are the random variables in a delay embedded phase space uncorrelated and independent?

Consider a smooth manifold $M=R^d$ embedded in a higher dimensional space $R^D$ using Takens Attractor reconstruction where $D > 2d+1$. Let, the Random Variable $X \in R^d$ have a Gaussian pdf and ...
4
votes
1answer
69 views

What is the interpretatation of individual contributions to the Shannon entropy?

If $X=\{ x_1,x_2,\dots,x_n\}$ are assigned probabilities $p(x_i)$, then the entropy is defined as $\sum_{i=1}^n\ p(x_i)\,\cdot\left(-\log p(x_i)\right).$ One may call $I(x_i)=-\log p(x_i)$ the ...
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0answers
16 views

Probabilistic interpretation of Hausdroff measure [closed]

My problem is to find/derive a pdf in terms of a parameter which closely resembles Hausdroff measure and the idea stems from the following concepts. Please correct me where I go wrong. Paper1 - ...
0
votes
1answer
75 views

Why are transition amplitudes more fundamental than probabilities in quantum mechanics? [duplicate]

I am reading Quantum Theory: Concepts and Methods by Asher Peres. Terminology used in the book: $P_{\mu m}$ are "transition probabilities". They are the squares of "transition amplitudes". That is, ...
2
votes
2answers
103 views

Probability of fluorescence: matching of binding energy and incoming radiation energy?

Assume an X-ray diffractometer equipped with a copper anode X-ray tube. When a sample containing cobalt, iron, or manganese is irradiated by copper's K$\alpha_1$ radiation, sample fluorescence becomes ...
0
votes
1answer
35 views

Empirical probability: what does it measure actually?

Empirical probability measures the probability of an event by thought experiment. But, by doing so, what information does it want to give? The experiment is done; so how can there be probability? The ...
0
votes
1answer
44 views

How to build a clock? [closed]

You have unreliable clocks that fire in the interval $(t,t+\delta)$ with probability density $f(t;\lambda)=\lambda\exp(-\lambda x)$. How will you build the best clock using these unreliable components ...
0
votes
0answers
93 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 $k_{B}$ ...
1
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2answers
118 views

Quantum Bayesianism and contradictory preditions of two agents

In quantum Bayesianism (QBsim) interpretation, the wave function $| \psi \rangle$, or density operator $\hat{\rho} = | \psi \rangle \langle \psi |$, is not objective. It is instead interpreted as the ...
0
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0answers
51 views

What is the cause for the validity of Statistical Regularity?

My book writes: From experience it has been observed that the value of frequency ratio gradually approaches a definite constant number when the no. of trial becomes larger & larger. This ...
3
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1answer
103 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 ...
1
vote
1answer
65 views

When everything follows strict laws in the universe, where does probability come from? [duplicate]

I am told that we can't predict whether we shall get a head or tail. We can only say that for an unbiased coin there is 50% probability for either. But coin is not case of Quantum Physics! I have ...
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0answers
63 views

What is a stochastic process in a physics context? [closed]

In my mind, a stochastic process is simply a "random" process, one where the outcome is informed by initial conditions but not in a deterministic way. Is this a correct definition? What are some ...
3
votes
2answers
118 views

How to calculate the tree-level probability amplitude for the electron-positron to muon-antimuon process?

Consider the following process: $e^+ + e^- \rightarrow \mu^+ + \mu^-$. I'm trying to calculate the probability amplitude of such a process in leading order. In leading order the amplitude is given ...
8
votes
3answers
429 views

How to work out the relation between the “mean relative speed” and the “mean speed”?

I'm a freshman and am taking the general physics course. I just learned intro thermodynamics. One problem that really puzzles me is the calculation of "collision mean-free path", where calculating the ...
0
votes
3answers
83 views

We don't know when a nucleus will decay. Then how can find its half life? [duplicate]

I mean how can we say that in 5730 years, 1/2 the no. of C14 nucleus will decay because in reality we don't know when a particular nucleus will decay
3
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2answers
133 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 ...
-2
votes
1answer
87 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 ...
1
vote
2answers
136 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
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4answers
55 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
80 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
554 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
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0answers
26 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
85 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> - ...
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2answers
92 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
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0answers
15 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 ...