# Potential operator for a particle in space

Considering a particle in 3d, the corresponding Hilbert space $$H$$ is the tensor product of individual Hilbert spaces

$$H=(H_x \otimes H_y \otimes H_z)$$

If the particle is in a potential $$V(x,y,z)$$ ,what is the corresponding potential operator for it?

If $$V(x,y,z)$$ has a development as a series in $$x,y,z$$, then the potential operator $$\hat V$$ is obtained by replacing $$x,y,z$$ in the series by the corresponding operators $$\hat x \otimes 1 \otimes 1, 1\otimes \hat y \otimes 1$$ and $$1\otimes 1 \otimes \hat z$$.
• $f (x, y) = f (a, b) + f_x(a, b) (x - a)$ what do I replace f(a,b) by? Mar 18 at 6:16