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1. Homework Statement

1. Homework Statement

I have two problems, but it's all related to the same main task. I have a state for the Hydrogen:

## \Psi = \frac{1}{\sqrt{2}}(\psi_{100} + i \psi_{211})##

where ## \psi_{nlm}##.

Use Heisenberg uncertainty relation to find the lower value for the varians ## \sigma_x ## of possible meassures for the electrons x-cordinate. HINT It can be used without proof that

## [L_z, x] = i \hbar y ##

**2. Equations**

Heisenberg:

## \sigma_x \sigma_y \geq \hbar/2##

**3. My try**

Well here is where it gets awkward. I have a very hard time understanding what i can use the hint for.

I could try to isolate ## \sigma_x \geq \frac{2}{\hbar \sigma_p}##

But given the hint is in a commutator i think i should use the generalized uncertainty principle.

##\sigma_A \sigma_B \geq |\frac{1}{2i} <[A,B]>| ##

But then i should look at

##\sigma_x \sigma_{L_z}##

Which makes no sense to me.

I Would very much appreciate your comment, thank you