# Tagged Questions

For questions about probability, probability theory, probability distributions, expected values and related matters. Purely mathematical questions should be asked on Math.SE.

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### Connection between Hamiltonian version of the least action principle and probability amplitude in the Schrödinger equation

If I'm not mistaken, SchrÃ¶dinger was influenced to look at wave equations because of de Broglie's assertion about particles having a wavelength. He started with the Hamiltonian equation which is ...
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### Quantum Mechanics: How to compute how fast must a function go to zero at infinity? [closed]

We say that the wave function must go to zero at infinity faster than $1/x^{0.5}$ in order for it to be normalizable. What about other quantities like the probability current? What is the general rule ...
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### Is the probability current an observable?

Is the probability current in Quantum Mechanics an observable? If so, how can it me measured (directly or indirectly)?
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### The Theoretical Minimum: Probability/Spin Question

Background In The Theoretical Minimum, it states that any spin state can be represented by a linear combo of the basis vectors $|u\rangle$ and $|d\rangle$ It then goes on to show how this is done ...
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### Why is the reflection coefficient in quantum mechanical scattering defined this way?

In Griffiths' "Introduction to Quantum Mechanics, second edition" section 2.5.2, p. 73, he states: For the delta-function potential, when considering the scattered states (with $E > 0$), we have ...
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### Fermi's golden rule and infinite probablity?

I am slightly confused about the application of Fermi's golden rule. Which during standard derivations indicates a probability of transitioning from the state $|i \rangle$ to the state $|f\rangle$ of: ...
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### Quantum Theory just lazy physics?

Is it true that physicists decided that because they couldn't predict with certainty the location of an electron at any given time, that they just created equations using probability instead, still ...
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### What is the probability of two bullets to get clashed? [closed]

I was surfing on Instagram, and I found this amazing proto whose description is "the probability of such an event to happen is incredibly small, so this is a really curious finding". Well.. I'm ...
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### Bell's Theorem - Why does $\lambda$ have a probability?

I'm reviewing Bell's theorem. In his proof by contradiction, he assumes the world is deterministic and defines a vector $\lambda$ as the set of all hidden variables which play a role in determining ...
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### Probability of finding electron in a spherical shell

In the book Arthur Beiser - Concepts of modern physics, probability of finding an electron in Hydrogen atom in the spherical shell between $r$ and $r+dr$ is given as P(r)dr = r^2|R(r)...
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### What is the probabililty that a fair coin lands on its side?

This is a popular gag in movies, but I wonder how likely it really is. What is the probability that a uniform cylindrical coin (with radius $1$ and height $h$) lands on its side? If the ground were ...
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### What is a quasi-probability distribution?

I have some questions about the quasi-probability distribution. What is it? And why it is important in quantum mechanics? And what does "quasi" mean?
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### Entropic forces in Brownian motion

Reading Entropic forces in Brownian motion I'm having trouble to understand how the author makes a computation. He needs to calculate the number of ways a particle that is released from the origin can ...
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### Boltzman equation for a collisionless medium?

In the derivation of the Boltzmann equation (link to Wikipedia) for a collisionless gas it is assumed that: f(\vec r+\frac{\vec p}{m} \Delta t, \vec P + \vec F \Delta t, t + \delta t)=f(\vec r, \...
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### In the algebraic formulation of Quantum Mechanics, how do probability amplitudes naturally arise?

In the algebraic formulation of quantum mechanics, consider $\mathcal{B}(\mathcal{H})$ as the set of all bounded operators on $\mathcal{H}$ (with involution, norm, etc.), which form a C*-algebra $C$. ...
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The following question is from General Problems on Physics by I.E Irodov 6.220. Find the decay constant and the mean lifetime of $^{55}\operatorname{Co}$ radionuclide if its activity is known to ...
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### Probability current: what's a good definition?

I am doing scattering problems with a really weird hamiltonian (e.g., only first-order in derivatives). I don't know how to define a probability current: I've looked at answers on this site, and they ...
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### How do we decide whether an electron orbital has a non-zero or zero probability of lying inside the nucleus of an hydrogen atom?

How do we decide whether an electron orbital has a non-zero or zero probability of lying inside the nucleus of an hydrogen atom? It is mostly from the radial function, as to what I think but how ...
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### Can a photon be absorbed by a proton?

When incident light passes through a hydrogen gas, for example, does it have 50% chance (since it's a 1:1 ratio of protons to electrons) of getting absorbed by the proton? Any chance at all? If no, ...
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### Probability that a measurement will be in some set

Let $\mathcal{H}$ be the Hilbert space of a quantum system and $A$ one observable in $\mathcal{H}$. If $A$ has discrete spectrum $\{a_n : n \in \mathbb{N}\}$ for simplicity, then by the postulates of ...
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### Many worlds probability of getting cancer [closed]

My understanding of probabilities in many worlds is following: If I would decide to start smoking and we know that 10% of smokers get cancer that means that in 10% of all worlds during my lifetime I ...
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### Measure-theoretic maths behind Born's probabilistic interpretation of Schrodinger's equation

I was reading a bit about Quantum Mechanics, Schrodinger's equation and its probabilistic interpretation (found this very insightful intro here https://plus.maths.org/content/schrodinger-1), my ...
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### Demonstration that the $\langle f(x)\rangle$ of an odd function $f(x)=-f(-x)$ of position $x$ in a symmetric potential well $V(x)=V(-x)$ is null

Consider a potential infinite well, which borders are $x=-a$ and $x=a$. I pretend to demonstrate that the expected value of a odd function $f(x)$, i.e., $\langle f(x)\rangle$, is null. We have the ...
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### Is there a mathematical basis for Born rule?

Wave function determines complex amplitudes to possible measurement outcomes. The Born Rule states that the probability of obtaining some measurement outcome is equal to the square of the ...
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### Pair annihilation - can annihilation be moderated?

I recently asked this question: How close does a particle-antiparticle pair need to be for annihilation to happen? And that received a good answer. But there was a second part to my question that ...
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### Can we predict throwing a dice?

What happens if we throw a dice from same position, with same force, by creating a vacuum environment on earth? Will it be predictable now i.e. will the dice have same results all the time? If answer ...
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### How close does a particle-antiparticle pair need to be for annihilation to happen?

I've most often seen the statement that the annihilation of a particle and its antiparticle occurs when they 'collide' with one another. So in other words when they get very close to one another right?...
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### Spin sums in cross sections. Summing amplitudes or probabilities?

The context: I'm calculating the cross section for a scalar particle to decay into a fermion-antifermion pair in Yukawa theory, at tree level. In doing this, when calculating the amplitude from ...
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### In what cases and with what method does one find a time dependent probability density for a quantum system in an infinite square well?

How can one find the time dependent probability density function of a quantum system given $\Psi(x,t=0)$? Say, $\psi(x) \sim x^4$ for $0 < x < L$. How can one find the time dependant probability ...
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### Problem in understanding Feynman's explanation of the Dirac-Delta function [duplicate]

This is quoted from Feynman's Lectures' Normalization of the states in $x$: We return now to the discussion of the modifications of our basic equations which are required when we are dealing with ...
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### Is quantum physics truly random or does it just appear that way because of Heisenberg uncertainty principle

The behavior of an electron (and other tiny things) is said to be probabilistic because we can't say where an election will be when we measure it, but only where it will probably be. As I understand ...
### Probability to find a particle in a particlar state $\psi_{n}$ [closed]
I have a problem to understand the probabilities in QM. In particular, if I have a particle in state $\psi_{n}$, then we change the system and we ask for the probability to find the particle in a ...