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1answer
82 views

Bohr's Correspondence Principle and the Born Rule

Bohr's correspondence principle and the Born rule are related right? The correspondence principle states that the behavior of systems described by the theory of quantum mechanics reproduces classical ...
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0answers
36 views

Converting a discrete statistical energy distribution to a continuous version

The probability of finding a particle at a particular energy level when energy is considered discrete is according to Boltzmann: $$P(E_j) = \frac{g_j\cdot e^{-\beta E_j}}{\sum_{j=1}^\infty g_j \cdot ...
3
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1answer
48 views

What does conservation of probability mean in Classical Mechanics and why is it true?

In the context of the Liouville equation, regularly the conservation of probability is invoked. (Of course, the overall probability is always conserved but this is a truism and not what is meant here. ...
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3answers
301 views

Probability of finding a particle in 1D box from classical view

The probability of finding a particle in a 1D-Box (from the classical view, the particle behaves as a particle but not a wave) is the same everywhere in the box. This seems to me quite ...
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0answers
36 views

How deterministic nature of our world emerges?

Quantum mechanics shows that nature is non-deterministic. But the world we see around us seems deterministic. Take for an example: harmonic oscillator when $n$ becomes very large the probability ...
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1answer
51 views

Free particle in one dimension, gaussian distribution question [closed]

Okay, so the question im struggling with is: Given a free particle in one dimension(with $H=\frac{p^2}{2m}$) in a state $p$ at $x=0$ with uncertainty $\sigma$(Gaussian Distribution) determine the ...
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0answers
84 views

Does Bell's theorem have anything to say about the locality or realism of Quantum Mechanics?

In the original paper written by Bell, it's clear to me that what he's really trying to answer is what class of Classical Theories (that obey the laws of classical probability theory) can replicate ...
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0answers
51 views

What is the Schrodinger equation's dynamics when having classical and statistical mechanics in mind?

Assume I take the following PDE without QM associated with it. $$ i\hbar\frac{\partial}{\partial t} \Psi(\mathbf{r},t) = \left [ \frac{-\hbar^2}{2\mu}\nabla^2 + V(\mathbf{r},t)\right ] \Psi(\mathbf{r},...
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0answers
288 views

Probability density to find the end of a double pendulum

Given infinite time, is there a way to find the probability to find the end of a double pendulum at a given position? I am looking at a system with no damping (constant energy). The bobs are point ...
2
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1answer
680 views

Position probability distribution of a particle in an infinite square well: classical versus quantum

The wave-function for a single particle in a potential well of width $L$ is given by the relation $$\Psi_n(x)=\sqrt{\frac 2L} \sin(K_n x)$$ where $K_n$ is $(n+1)\pi/L$ and $n$ is a positive integer. ...
3
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1answer
157 views

Particle with normally distributed initial position and velocity

Some time ago I asked myself, "suppose I have a particle and I know its velocity and initial position are normally distributed; what is the distribution of its position after a period of time $\Delta ...
2
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2answers
526 views

Double Slit Experiment/Transition of Classical to Quantum problems in Probability Addition in “An Experiment on bullets”

The First Picture is taken out from the Book The Character of Physical Law By Richard Feynman And the second picture is from his own The Feynman Lectures on Physics. Both figures correspond to the An ...
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4answers
626 views

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

If I'm not mistaken, Schrödinger 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 ...
3
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1answer
283 views

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 ...
0
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0answers
60 views

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 ...
9
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2answers
708 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.
4
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1answer
328 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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2answers
6k views

Particle in a 1-D box and the correspondence principle

Consider the particle in a 1-d box, we know very well the solutions of it. I'd like to see how the correspondence principle will work out in this case, if we consider position probability density ...
10
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1answer
1k views

Quantum version of the Galton Board

If classical particles fall through a Galton Board they pile up in the limit of large numbers like a normal distribution, see e.g. http://mathworld.wolfram.com/GaltonBoard.html What kind of ...
2
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1answer
510 views

Classical mechanics from Quantum mechanics

I'm looking at a way to prove that one recovers, under ad hoc assumptions, classical mechanics from quantum theory. Usually, we can find in textbooks that the propagator $$K(x,x_0;t)=\langle x|e^{-i ...
4
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3answers
2k 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 ...
2
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3answers
327 views

Effect of surface treatment on fair dice

If I have a perfectly balanced and thus fair cubic die, then polish 3 adjacent faces (so that their coefficient of friction is effectively zero) and roughen the remaining faces (so that their ...
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2answers
2k views

How can you test to see if a dice is weighted?

I was browsing Etsy today and came across this. What tests are there to see if the dice are usable, ie, if one side isn't favored over another, and if all sides are balanced? Would this just be to ...
3
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4answers
3k views

“Regular” 20-sided die, vs “life counter” 20-sided die. Same probabilities?

Regular dice are made such that opposite sides of the die add to 1+the number of sides. For example, a 20-sided die has 14 and 7 opposite of each other, adding to 21. For certain types of games, "...