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- What is a good definition for Radial Probability Density?
The volumic probability density $|\Psi|^2$ peaks at the center, but remains finite there The tridimentional integration of this quantity over all space gives one What is called the "radial probability density" is the volumic density already integrated in the infinitesimal spherical shell between two spheres, $4 \pi r^2 |\Psi|^2$
- Differences between wavefunction, probability and probability density?
Probability Density Probability density is a concept that naturally arises whenever you talk about probability in connection with a continuous variable, such as position of a particle In contrast to discrete probability (such as idealized coin-flipping or dice-rolling), we can't directly assign a probability to each individual outcome
- Form of Schrödinger equation for the probability density
It is interesting that the relative simple probability density of say a 1s electron in hydrogen is a solution of this very tedious equation $\endgroup$ – Jan Bos Commented Dec 7, 2017 at 12:55
- quantum mechanics - Probability vs radial probability density - Physics . . .
And when you compute the probability density (or in other words the electron distribution density) you are calculating the likelihood of finding electron in the vicinity of a PARTICULAR POINT, which btw hurts the wave-particle duality characteristic of an electron
- Classical and quantum probabilities in density matrices
Now, if we also agree that probabilities of different, mutually excluding states (eigenstates of the density matrix) may be calculated as eigenvalues of the density matrix, and if we assume that there is a smooth formula for probabilities of some properties, then it also follows that even pure states – whose density matrices have eigenvalues
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