I have some point $a$ with coordinates $(r,\theta, \phi)$. I can define the position vector from the origin to $a$, simply as $a^i = (r,\theta,\phi)$.

At the same point $a$, there is also some momentum vector $p_i = (p_r, p_{\theta}, p_{\phi})$.

I want to calculate the angle between these two vectors. IF everything was in Cartesian coordinates I could simply do a dot product and calculate the magnitudes of vectors $a^i$ and $p_i$.

My question is how do I do that in spherical polars?

Clearly, I can convert $a^i$ to Cartesian coordinates simply enough, but how would I do the same with the momentum vector? Alternatively, can it be done just staying in spherical polar coordinates?


Note that assuming

$$\vec p=p_r\vec e_r+p_{\theta}\vec e_{\theta}+p_{\phi}\vec e_{\phi}$$

we have that $\vec a_i$ is aligned to $\vec e_r$ and therefore the angle between $\vec a_i$ and $\vec p_i$ is equal to the angle between $\vec p_i$ and $\vec e_r$ that is



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.