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-1
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2answers
405 views

A proton is trapped in an infinitely deep well of L meters. The proton is in the first excited state. How does the excited state change the question.

The real question was: A proton is trapped in an infinitely deep well of 1*10^-14m. I suppose that is unimportant as that should only help us decided the limits of our integration. What I'm worried ...
4
votes
1answer
91 views

Convexity — reference request

I've been reading a few papers on generalized probabilistic theories, and have been struggling through proofs of some results that involve use of convexity and group theory, e.g. this paper on bit ...
0
votes
1answer
834 views

Plotting Hydrogen's $2P_{x,y,z}$ Probability Densities in MATLAB [closed]

I have spent an unreasonable amount of time trying to plot $F(r,\theta,\phi)$ plane slices in MATLAB. I want to look at $x-y,y-z,x-z$ planes. Here's the function, specifically: ...
6
votes
1answer
92 views

Allowed states vis-a-vis allowed dynamics in generalized probabilistic theories (GPTs)

In his work on information processing in GPTs http://arxiv.org/abs/quant-ph/0508211 Barrett speculates that the trade-off between allowed states and the allowed dynamics in a GPT is optimal in quantum ...
1
vote
2answers
442 views

Hydrogen 2P Probability Density Question

I'd like to calculate the probability density for Hydrogen in the $|2,1,1\rangle$ and $|2,1,-1\rangle$ states. There is an $\exp(\pm i\phi)$ term attached to the wave function for these states. It ...
1
vote
2answers
916 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
votes
1answer
630 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 ...
7
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3answers
1k views

Relation between unitarity and conservation of probability

In a seminar, I heard that the unitary aspect of representations was important physically, because in quantum mechanics unitarity is closely tied to the conservation of probability. Could someone ...
2
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1answer
2k views

Probability current

Conservation of probability: Suppose a wavefunction has ${\partial \mathbb P \over \partial t} = -t f(x,t)$ and ${\partial j \over \partial x} = i f(x,t)$. How does it follow that ${\partial \mathbb P ...
4
votes
1answer
254 views

Young's double slit

Am I right to think the (general) probability distribution of photon in a double slit experiment at the screen has the form $|\psi|^2 = c e^{\alpha x^2}\cos^2(\beta x)$? (Due to the superposition of ...
12
votes
2answers
255 views

Random Walk Randomly Reflected

Hi I am not specialist in probability so I will not be surprised if the answer for this question is just a simple consequence of well known results from the random walk theory. In this case, I will ...
2
votes
5answers
5k views

Is it true that quantum mechanics technically allows anything to happen?

Maybe this is a silly question (I think it is), but it's a question I'm arguing with some of my friends for a long time. The ultimate question is: Is everything (in our Universe) possible ? I've ...
20
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5answers
209 views

Connections and applications of SLE in physics

In probability theory, the Schramm–Loewner evolution, also known as stochastic Loewner evolution or SLE, is a conformally invariant stochastic process. It is a family of random planar curves that are ...
3
votes
2answers
603 views

an example of a quantum system for which wigner function transitions to negative values

I want to check my understanding of the Wigner transform and try to understand why and how exactly the probabilistic interpretation drops down as the function goes to zero and then to negative values ...
21
votes
2answers
123 views

Bell polytopes with nontrivial symmetries

Take $N$ parties, each of which receives an input $s_i \in {1, \dots, m_i}$ and produces an output $r_i \in {1, \dots, v_i}$, possibly in a nondeterministic manner. We are interested in joint ...
4
votes
1answer
190 views

Products of Gaussian stochastic process variables

In the classic experimental physics text "Statistical Theory of Signal Detection" by Carl. W. Helstrom, Chapter II, section 4 concerns Gaussian Stochastic Processes. Such a process is observed at ...
3
votes
4answers
2k 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, ...
11
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1answer
538 views

The measure problem in the anthropic principle

The anthropic principle is based upon Bayesian reasoning applied to the ensemble of universes, or parts thereof, conditioned upon the existence of conscious observers. That still leaves us with the ...