Quick question: Momentum operator in QM

[Libohove90]

Homework Statement

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?

Homework Equations

The two I gave above.

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!

 

[Libohove90]

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

 

[Fightfish]

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

 

[Intrastellar]

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

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

 

[kevinferreira]

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

 

[CompuChip]

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