# Orbital angular momentum of an electron in s-orbital

I'm a beginner in quantum mechanics, and I'm pretty much confused with the orbital angular momentum of electron in s-orbital of hydrogen atom. I've read that average angular momentum of an electron in $$1s$$ orbital of $$\ce{H}$$-atom is $$0 \pu{kgm^2s^-1}$$, but when I took the wave function of $$1s$$ orbital of $$\ce{H}$$-atom and solving by the following way is giving me instantaneous angular momentum is $$0\pu{kgm^2s^-1}$$.

My way of solving:

The momentum operator is $$\hat p = -i\hbar\nabla$$ and the $$\psi_{1s}= k \times e^{\frac{-r}{a_0}}$$, where $$k$$ is normalizing constant

Applying momentum operator for $$1s$$ orbital,

$$\hat p \psi_{1s} = p \psi_{1s}$$ I'm getting some thing like $$\hat p \psi_{1s} = -(x \hat i+ y\hat j+z\hat k)k^{'}e^\frac{-r}{a_0}$$, which implies that the momentum $$\overrightarrow p$$ of electron in $$1s$$ orbital is $$\overrightarrow p = k^{''}(x \hat i + y \hat j + z \hat k)$$

So, angular momentum can now be given by $$\overrightarrow L = \overrightarrow r \times \overrightarrow p$$ The position vector $$\overrightarrow r = x\hat i + y\hat j + z\hat k$$

As the position vector, $$\overrightarrow r$$ and the momentum vector, $$\overrightarrow p$$ are in anti-parallel directors at every point in space, I have concluded that $$\overrightarrow L = \overrightarrow 0$$ at every instant, which contradicts to what I've read.

(NOTE: The source from where I've read is not very much reliable, but I didn't find any thing related to this any where else)

• So you've read that it should be $0$ and also found it to be $0$. What's the problem? Sep 19, 2021 at 7:43
• @IvanNeretin I've read average angular momentum is zero but I got instantaneous also zero as well. Is it correct? Sep 19, 2021 at 7:45
• Does it make the average different from $0$? No. So, there is no contradiction. Sep 19, 2021 at 7:47
• @IvanNeretin It doesn't make any thing different, but is the instantaneous value also $0$? Sep 19, 2021 at 7:48
• Yes.$\mathstrut$ Sep 19, 2021 at 7:49