Eigenvalues of positions in atomic orbitals

In summary, the conversation discusses the number of possible position eigenvalues for a hydrogen atom with a single electron in an x, y, z coordinate. It is determined that there is an uncountably infinite number of continuous position eigenvalues and there is no formula to calculate them. Instead, the probability density of a position measurement outcome can be computed using the magnitude-square of the position wavefunction.
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lucas_
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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?
 
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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.
 
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1. What are eigenvalues of positions in atomic orbitals?

Eigenvalues of positions in atomic orbitals refer to the quantized energy levels of an electron occupying a specific position in an atomic orbital. They describe the probability of finding an electron at a particular location in an atom.

2. How are eigenvalues of positions in atomic orbitals calculated?

Eigenvalues of positions in atomic orbitals are calculated using mathematical equations that take into account the wave function and potential energy of the electron in the atom. The solutions to these equations give the allowed energy levels, or eigenvalues, for a given atomic orbital.

3. What is the significance of eigenvalues of positions in atomic orbitals?

The eigenvalues of positions in atomic orbitals are significant because they determine the electronic structure and properties of atoms. They also play a crucial role in understanding the behavior of electrons and their interactions within atoms.

4. How do eigenvalues of positions in atomic orbitals relate to electron energy levels?

The eigenvalues of positions in atomic orbitals correspond to the energy levels of electrons in an atom. Each eigenvalue represents a specific energy level that an electron can occupy in an atomic orbital. The higher the energy level, the farther away the electron is from the nucleus.

5. Can eigenvalues of positions in atomic orbitals change?

Yes, eigenvalues of positions in atomic orbitals can change under certain conditions, such as when an external force is applied to the atom or when the atom undergoes a chemical reaction. These changes can affect the electron's energy levels and alter the electronic structure of the atom.

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