About momentum operator in other coordinate system

[KFC]

Hi there, does anyone know where can I found a material or note about how to deduce momentum operator in coordinate system other than linear coordinate (especially in spherical coordinate system)?

Thanks in advanced.

 

[George Jones]

Hi there, does anyone know where can I found a material or note about how to deduce momentum operator in coordinate system other than linear coordinate (especially in spherical coordinate system)?

Thanks in advanced.

Express the other coordinates in terms of $x$, and $y$, and $z$, and then use the chain rule. For example,

$$\frac{\partial}{\partial x} = \frac{\partial r}{\partial x}\frac{\partial}{\partial r} + \frac{\partial \phi}{\partial x}\frac{\partial}{\partial \phi} + \frac{\partial \theta}{\partial x}\frac{\partial}{\partial \theta}.$$