- #1

dingo_d

- 211

- 0

## Homework Statement

I have to proove:

[tex][\hat{y},\hat{p}_y]=[\hat{z},\hat{p}_z]=i\hbar\hat{I}[/tex]

## Homework Equations

[tex][\hat{A},\hat{B}]=\hat{A}\hat{B}-\hat{B}\hat{A}[/tex]

## The Attempt at a Solution

Ok so I know that

[tex][\hat{y},\hat{p}_y]=\hat{y}\hat{p}_y-\hat{p}_y\hat{y}=y\left(-i\hbar\frac{\partial}{\partial y}\right)-(-i\hbar\frac{\partial y}{\partial y})=i\hbar[/tex]

Analogus for z component. But how to show that it's [tex]i\hbar\hat{I}[/tex]?

Since they're operators they can be expressed in component form - they correspond to some kind of matrix, right?

I don't see how to get that [tex]\hat{I}[/tex] :\