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1answer
250 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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1answer
89 views

Random walks on resistive network

I have been referring to a paper http://arxiv.org/abs/physics/0405135 to determine the effective resistance using random walks for an infinite square resistive lattice Though the author seems to ...
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0answers
23 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 ...
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2answers
265 views

Fermi-Dirac Statistics

In Fermi-Dirac statistics the probability of being in a certain energy state is $$f(E) = \left[1 + \exp\left(\frac{E-E_F}{k T}\right)\right]^{-1}$$ In the area that I'm looking at the texts always ...
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0answers
43 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 ...
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1answer
45 views

What do matrices in the Gaussian orthogonal ensemble look like?

I've been reading a fair amount about quantum chaos, and random matrix theory comes up a lot. I get that they're looking at the distribution of eigenvalues from an ensemble of random matrices, but I ...
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1answer
97 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 ...
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0answers
56 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 ...
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2answers
40 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 ...
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0answers
23 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 ...
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1answer
72 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?
3
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1answer
34 views

Probability of measuring momentum [closed]

Suppose we have this wavefunction: $$ \psi = A \left( cos(kx) + cos (2kx) \right) $$ I have to find the possible results of measurement of momentum and their probabilities. Attempt For a momentum ...
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7answers
1k views

Mathematically possible vs physically probable outcomes

A good buddy of mine and I have had a friendly debate about the origins of the current state of our universe (namely; Earth and life on Earth) and have fundamentally disagreed in our stances with ...
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0answers
9 views

Conceptual questions about chaotic signals

Are chaotic signals stationary or non stationary signals? They are ergodic and ergodic signals are a kind of stationary signals. But, from statistics point of view, are chaotic signals classified as ...
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1answer
100 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
48 views

tritium beta decay - probability of being in 1s state

Hydrogen-like wavefunctions have the form: $$R_{10} = \left(\frac{Z}{a_0}\right)^{\frac{3}{2}} 2\space e^{-\frac{Zr}{a_0}}$$ $$Y_{00} = \frac{1}{\sqrt {4\pi}} $$ where $a_0 = \frac{4\pi \epsilon_0 ...
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1answer
27 views

Change of variables in calculating the integral of multivariable differential entropy

I have already asked this question in math.SX but here might be more proper. So I decided to put a copy here and delete the one which is not the one that got an answer: I know that for one ...
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7answers
1k views

Why is the application of probability in QM fundamentally different from application of probability in other areas?

Why is application of probability in QM fundamentally different than application of probability in other areas? Quantum mechanics applies probability according to the same probability theory that ...
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1answer
472 views

Is it really impossible to calculate in advance the result of throwing dice?

Is it really impossible to calculate in advance the result of throwing dice? After all, the physics of dice throwing is in the world of classical mechanics, rather than quantum mechanics.
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0answers
66 views

Probability density of Klein-Gordon equation

This may, perhaps, stir some healthy debate; at least I am having some "fun" thinking about it, hopefully I can solicit some outside views too. It is often regarded that the Klein-Gordon equation ...
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0answers
61 views

Reference for stochastic processes which helps moving from a basic level to a measure theory one

I'm looking for a reference (books, notes, lectures) which helps a physicist to understand the language of measure theory in the context of stochastic processes (in particular markov chains). I've ...
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3answers
133 views

Intuition/derivation behind the probability current definition

The definition is: $${\bf{j}} = \frac{\hbar}{2mi} (\psi^* \nabla \psi - \psi \nabla \psi^*)$$ However: Where ever I have looked, the above "pops out of nowhere". I was wondering how can I obtain ...
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0answers
35 views

Measurement of the amplitude

I want to ask how do we actually measure the probability amplitude that appears in Schrödinger equation. From what I read in quantum mechanics textbooks, it appears that after the measurement, the ...
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1answer
24 views

Reflection Probability for Different Potentials - Quantum Mechanics

My question is above. Firstly, I don't actually know whether it is true or not (!). Secondly, if I were to try to prove it, then I have very little idea how to. The potential steps that I have ...
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3answers
137 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 ...
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0answers
38 views

Deriving probability distributions from the Wigner distribution

I know that I can calculate the probability distributions of $x$ and $p$ from the Wigner quasiprobability distribution, and I can calculate the probability distributions of other operators by ...
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4answers
178 views

Probability and the many-worlds interpretation

If I toss a coin, then according to the many worlds interpretation of QM, in half those worlds I'll get a head. If I then toss again, then in a quarter I will have got two heads. And so on. There will ...
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2answers
109 views

Interpreting the Partition Function and Free Energy Mathematically

Given that The partition function in statistical mechanics tells us the number of quantum states of a system that are thermally accessible at a given temperature ...
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0answers
44 views

Quantum Rigid Rotor Perturbation

As the title says, I have a rigid rotor with a perturbation given below $$H=\frac{L^2}{2I}-\alpha B L_z.$$ So I know that the eigenvalues of $H$ will be $\ell(\ell+1)/2I -\alpha B m$ where $m$ is our ...
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2answers
295 views

Why was quantum mechanics regarded as a non-deterministic theory?

It seems to be a wide impression that quantum mechanics is not deterministic, e.g. the world is quantum-mechanical and not deterministic. I have a basic question about quantum mechanics itself. A ...
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2answers
1k 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? ...
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3answers
191 views

What is a linear probability density function?

In the following question, what is meant by linear probability density function? Is it a uniformly distributed variable or triangularly distributed? Thanks in advance. The kinetic energy of any ...
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3answers
125 views

Probability distribution in phase space and Liouville's theorem?

We can define a probability distribution over phase space (say 1D) $\rho(x,p)$ such that, for example, $$\langle x\rangle = \int x \rho(x,p) dxdp$$ etc. It can be shown here that such a distribution ...
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1answer
87 views

Why don't we need to normalize wavefunction to find probability distribution?

Consider an unormalized wavefunction of a rotor at $t = 0$, a combination of $n=0$ and $n=2$ states: $$\psi(\phi) = 3 - 2 \cos (2\phi).$$ Find the probability distribution in angle. The ...
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0answers
26 views

How do I overlap this two-particle symmetric wavefunction?

Suppose we have a symmetric wavefunction that composed of a two-particle system: $$ \psi_s = \frac{1}{\sqrt 2} \left(|u,A\rangle|v,B\rangle + |v,A\rangle|u,B\rangle\right)$$ where $u_{(x)}$ and ...
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1answer
87 views

Is there a known equation for evolution of classical particle probability density?

Suppose we have some very imprecise knowledge of classical particle's coordinates and momentum: what we can only tell is the probability density to find it in some point of phase space. This is ...
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0answers
67 views

Ising model. What is large fluctuations of magnetization?

My background is in mathematics. I have studied the Ising model in $\mathbb{Z}^2$. The main model of statistical mechanics. Yesterday, I was reading the preliminary notes of the book Statistical ...
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1answer
277 views

Kolmogorov-Smirnov test vs Chi-squared test

What is the difference between the Kolmogorov-Smirnov test and the Chi-squared test? When should we use one instead of the other? I was reading this article, and I got confused a lot. It is hard to ...
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1answer
542 views

Transmission and reflection

What is the transmission amplitude of a wavefunction $\phi(x)=e^{ikx}(\tanh x -ik)$? I would have thought that it is $\tanh x -ik$ since this is the factor associated with the forward travelling ...
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3answers
222 views

Why is $|\Psi|^2$ the probability density?

I am starting with Quantum Mechanics, learning online. I can't seem to find the reason for $|\Psi|^2$ being the probability density of finding an electron. They've just taken it for granted ...
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3answers
632 views

Born's Rule, What is the Reason?

As far as I've read online, there isn't a good explanation for the Born 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
252 views

Calculating the most probable radius for an electron of a hydrogen atom in the ground state

This link describes a method for determining the most probable radius of an electron for a Hydrogen atom in the ground state. It states that : The radial probability density for the hydrogen ...
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3answers
402 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 ...
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2answers
36 views

Calculating the Probability Current of a Travelling Wave

Calculate the probability current density vector $\vec{j}$ for the wave function : $$\psi = Ae^{-i(wt-kx)}.$$ From my very poor and beginner's understanding of probability density current it is : ...
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1answer
35 views

Can electrons coincidentally flow along a circuit to cause current?

My understanding of circuits which are not supplied an e.m.f. is that the electrons randomly just flow about in random directions, and since there's so many of them, probability dictates that any ...
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2answers
103 views

Free-particle solution to Schrödinger Equation

The free particle solution in stationary state (with definite energy) to the Schrödinger equation is $$\psi(x,t) =Ae^{i(kx-\omega t)} + Be^{-i(kx+\omega t)}$$ Since the energy is definite, and ...
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2answers
638 views

What is probability current in quantum mechanics?

What is probability current in quantum mechanics? Why define such a thing? I mean the meaning of probability current. I know the formula for it but I just don't get the idea of a flow of probability ...
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3answers
401 views

What is the relationship between Maxwell–Boltzmann statistics and the grand canonical ensemble?

In the grand canonical ensemble one derives the expectation value $\langle \hat n_r\rangle^{\pm}$ for fermions and bosons of sort $r$: $$ \langle \hat n_r\rangle^{\pm} \ \propto \ ...
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4answers
5k 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, ...
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2answers
150 views

Does quantum randomness predicate an infinite number of realities?

I am a layman when it comes to physics and especially quantum mechanics. I have seen many documentaries on the subject, and often in these productions there is a physicist featured explaining the ...