# Questions tagged [probability]

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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### Probability of observing harmonic oscillator at a particular position

Consider a classical harmonic oscillator whose Hamiltonian is $$H=\frac{p^2}{2m} +\frac{1}{2}mw^2x^2$$ where $w$ is the oscillating frequency. I wish to find the probability of observing the harmonic ...
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### Quantum measuring simulation

Hi I want to understand a concept that I been thinking about. I'm trying to simulate the energy measurement of a system (a many body quantum system to be precise), and I'm trying to simulate a quantum ...
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### What is an intuitive or simple proof of Gleason's theorem and how it relates to the Born rule?

What is an intuitive or simple proof of Gleason's theorem and how it relates to the Born rule? I tried to read the articles, but the proof seemed big and the kind that are unintuitive (im not ...
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### Can this shape of matrix elements in the path integral formalism be linked to some sort of expectation value?

This question is about expressions of the form $$\langle x_f, t_i | \hat{x}(t) | x_i, t_i \rangle = \frac{1}{N} \int_{x(t_i) = x_i}^{x(t_f) = x_f} \mathcal{D} x~x(t)e^{i S[x]}.$$ In the following ...
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### Why sum of squares of the magnitudes of Fourier coefficients in Infinite Square Well equals one but it is not so in regular Fourier analysis?

My question is basically this.. In regular math, Fourier Coefficients give the "amount" a particular frequency is available in any periodic signal. The squares of sum of coefficients is not ...
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### Why is there a non-zero probability density of finding an $l=0$ electron at the origin of a Hydrogen-like atom?

A well known result for the $l=0$ hydrogenic functions is that $$\psi_{nlm_l}=R_{nl}(r)Y_{lm_l}$$ $$|\psi_{n00}|^2=\frac{Z^3}{\pi a_0^3n^3}$$ where $R_{nl}$ and $Y_{lm_l}$ are the radial function and ...
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### Neutrino Oscillation and Probability

I am a fresher in a university pursuing physics major. I have been very passionate about neutrinos. So, I started studying them. But I have realised that, it requires a lot of mathematical physics ...
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### Integrate continuity equation in QM

From Shankar's QM book pg. 166: The continuity equation for probability density in QM is $$\frac{\partial P(\vec{r},t)}{\partial t}=-\nabla \cdot \vec{j}(\vec{r},t),$$ where $P=\psi^*\psi$ is the ...
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### If frequency of photons is a continuous spectrum, wouldn't the chance of a photon having the exact right frequency to excite an electron be zero?

As far as I'm aware, the energy needed to excite an electron to a different orbital is discrete. Since the frequency of light is continuous, wouldn't it be impossible for a photon to have the exact ...
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1 vote