# Quick question: Momentum operator in QM

1. Feb 1, 2013

### Libohove90

1. The problem statement, all variables and given/known data

There are two ways to write the momentum operator, p = (-i hbar d/dx) and p = (hbar / i)d/dx. How do you go from one to the other?

2. Relevant equations

The two I gave above.

3. The attempt at a solution

I tried to see if -ih = h/i by squaring both sides, but one came out positive and the other negative. Thanks for the help!

2. Feb 1, 2013

### Libohove90

-i^2 = 1, not -1. This makes (-i hbar)^2 not equivalent to (hbar / i)^2

Last edited: Feb 1, 2013
3. Feb 2, 2013

### Fightfish

Since when did $(-i)^2 = 1$?

4. Feb 2, 2013

### Intrastellar

$(-i)^2 = (-1)^2(i)^2$

5. Feb 2, 2013

### kevinferreira

$i^{-1} =- i$
Why?
$$i^{-1} = e^{-ln(i)}=e^{-ln(e^{i\pi /2})}=e^{-i\pi /2}=-i$$
since $e^{\pm i\pi /2}= cos(\pm\pi /2) + isin(\pm\pi /2)=\pm i$

6. Feb 2, 2013

### CompuChip

Or you just multiply 1/i by i/i to get i/i^2 = i/(-1) = -i.