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Quantum mechanics

What's the difference between the radial wave function and radial distribution function? Don't they both consider the probability of finding the electron at distances away from the nucleus?

Reply 1

Manitude

Off the top of my head the distribution function is the normalised wave function so that integrating over all space gives a probability of one (I.e. The particle exists somewhere). I may be wrong of course, as it's been almost four years since I studied QM and it's a bit hazy for me. Uncertain, one might say.

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Reply 2

Unkempt_One

Is this question in a Chemistry context? There seem to be two definitions floating around, which sort of but don't mean the same thing. In Chemistry, it refers to the probability density for an electron to be found at a distance r from the nucleus in a given orbital. To find it, take the radial wave function, take the modulus squared and multiply it by the surface area 4pir^2.

By the way. In this case the normalisation would be that the integral of 4pir^2|radial wavefunction|^2 over all possible radii is one. In physics the definition would be that the integral of r^2|radial wavefunction|^2. The choice of convention is completely arbitrary.

(edited 8 years ago)

Reply 3

Charmant

Original post by Rydberg97

What's the difference between the radial wave function and radial distribution function? Don't they both consider the probability of finding the electron at distances away from the nucleus?

The radial wave function (psi) simply shows the shape of the wave that belongs to the electron. When squared this gives the probability of finding an electron in a tiny box (with dimensions dx dy dz) at a distance r from the nucleus. This function suffers from the problem that the number of these tiny boxes varies with r and can produce results with a high probability of finding the electron *in* the nucleus! Chemists often prefer to use the radial distribution function 4pi (r)2 (psi)2 which gives the probability of finding the electron within a (very thin) spherical shell of thickness dr at distance r from the nucleus.