Eigenvalues of positions in atomic orbitals

[lucas_]

Let's take a hydrogen atom with a single electron. How many eigenvalues of position can it form (assuming you put it the atom in an x, y, z coordinate)? like 1 billion possible position eigenvalues? Is it continuous number like 1.1, 1.2, 1.3 or quantized? and either case, how many eigenvalues can it form, what's the formula to compute for it?

 

[jfizzix]

the position eigenvalues (i.e., the number of possible position measurement outcomes) are continuous for any orbital. There is an uncountably infinite number of them (like the number of values between zero and 1).

There is no formula to speak of to find the set of possible position measurement outcomes, since it's usually just all of them. What you can do is compute the probability density of a position measurement outcome, and that is the magnitude-square of the position wavefunction.