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In the position representation the momentum operator takes the form of the gradient, $-i\hbar \nabla$.

It is understood that its components denote $p_{x}, p_{y}, p_{z}$ respectively; but, when transforming the gradient to spherical coordinates, what do the individual radial, polar and azimuthal components represent?

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    $\begingroup$ Possible duplicates: physics.stackexchange.com/q/9349/2451 , physics.stackexchange.com/q/224027/2451 and links therein. $\endgroup$
    – Qmechanic ♦
    Commented Mar 17, 2023 at 18:15
  • $\begingroup$ Useful background. $\endgroup$
    – Cosmas Zachos
    Commented Mar 17, 2023 at 20:18
  • $\begingroup$ Can you sharpen your question? Which aspect of the conversion are you seeking to enlighten? Are you aware of the conversion formulas? $\endgroup$
    – Cosmas Zachos
    Commented Mar 17, 2023 at 20:24
  • $\begingroup$ So for example looking at the gradient in spherical coordinates, the radial component of the vector is not thought of as the expected classical radial momentum. Nevertheless this radial component appears in the momentum operator in spherical coordinates. So my question is what does it represent? $\endgroup$
    – IdentityOne
    Commented Mar 18, 2023 at 10:08
  • $\begingroup$ Something bothering you about the linked answers? Are you fully comfortable with the appendix of the linked paper? $\endgroup$
    – Cosmas Zachos
    Commented Mar 18, 2023 at 10:53

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