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Hello,

I hope you are doing well.

I had a question about the eigenvalue problem of quantum mechanics. In a past class, I remember it was strongly emphasized that the eigenvalues of an eigenvalue problem is what we measure in the laboratory.

##A\psi = a\psi##

where A would be the operator and the 'a' would be the eigenvalue.

I've also seen some books use the "polar" form of the wavefunction, where:

##\psi = Re^{iS/\hbar}##

This is often used in de Broglie-Bohm models of QM to get the "quantum" Hamilton-Jacobi equation. What I wanted to ask is this: If we assume that R is a function of position and time (as is done in the de Broglie-Bohm approach), doesn't this violate the eigenvalue problem?

Because then we get extra terms that come from the derivatives of the amplitude once acted upon by the momentum or energy operators. This is something I've been giving some thought, and it has been bothering me. If you have some insight to share, that would be much appreciated.

Many thanks.

All the best!

I hope you are doing well.

I had a question about the eigenvalue problem of quantum mechanics. In a past class, I remember it was strongly emphasized that the eigenvalues of an eigenvalue problem is what we measure in the laboratory.

##A\psi = a\psi##

where A would be the operator and the 'a' would be the eigenvalue.

I've also seen some books use the "polar" form of the wavefunction, where:

##\psi = Re^{iS/\hbar}##

This is often used in de Broglie-Bohm models of QM to get the "quantum" Hamilton-Jacobi equation. What I wanted to ask is this: If we assume that R is a function of position and time (as is done in the de Broglie-Bohm approach), doesn't this violate the eigenvalue problem?

Because then we get extra terms that come from the derivatives of the amplitude once acted upon by the momentum or energy operators. This is something I've been giving some thought, and it has been bothering me. If you have some insight to share, that would be much appreciated.

Many thanks.

All the best!

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