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## Summary:

- How is it possible to rotate a function (for example the 3D wave function) by an infinitesimal angle by using derivatives?

## Main Question or Discussion Point

I was solving a problem for my quantum mechanics homework, and was therefore browsing in the internet for further information. Then I stumbled upon this here:

R is the rotation operator, δφ an infinitesimal angle and Ψ is the wave function.

I know that it is able to rotate a curve, vector... with a rotation matrix. But how is it possible to rotate a function only with derivatives? I tried to rephrase a function f(x) as a curve, applying the 2D rotation matrix and small angle approximation and convert it back to an explicit function f(x). But I did not get the same answer.

My question is now: how does this work and what’s the connection to the rotation matrix?

I am really thankful for every help!

R is the rotation operator, δφ an infinitesimal angle and Ψ is the wave function.

I know that it is able to rotate a curve, vector... with a rotation matrix. But how is it possible to rotate a function only with derivatives? I tried to rephrase a function f(x) as a curve, applying the 2D rotation matrix and small angle approximation and convert it back to an explicit function f(x). But I did not get the same answer.

My question is now: how does this work and what’s the connection to the rotation matrix?

I am really thankful for every help!