Help with Chem please!
Ok wait so is the probability density |ψ|² or is it |ψ><ψ|?
Im confused cause my teacher said they are the same thing but
|ψ|² is ψ*ψ, where ψ* is the conjugate
However
|ψ><ψ| is the integral of ψ*ψ dτ right???
So which one is it and why?
(Im pretty sure its |ψ><ψ| but then what does ψ² represent?)
Move over loser *cracks knuckles*
Ok so!
Ψ is a wave function, it has a ton of useful information but we cant get to it without an operator (pfft pathetic)
Ψ can have an imaginary part, and therefore does not have a physical real meaning, so what happens if we do this?? Ψ*Ψ BOOM ITS REAL NOW
(Cuz Ψ* is the conjugate which means that if the original function had an imaginary part i, multiplying it be its conjugate is i×-i AND THATS??? THATS RIGHT 1 (one) so now its reaaaal)
So Ψ*Ψ is real and its a probability density function... wth is that? No clue idk math ok?
So THEN we can integrate it, since that is the area under the function that is INDEED the probability of finding a particle in a given space!!
So lets see...
Ψ² = Ψ*Ψ ONLY if Ψ didnt have a complex (imaginary) part in the first place, so lets ignore Ψ² cuz its not very correct
Ψ*Ψ is real and its a probability density function but its still not that exiting
But if we do THIS <Ψ|Ψ> (aka we integrate Ψ*Ψ) THEEEN we get the probability of finding an electron
Last but not least, if i look for the electron dτ, meaning in aaaaall the space, what is the probability of me finding it? 100%
100% why? Well i might not know where that little fucker is hiding but i know for a fact that it is SOMEWHERE
So if i look everywhere? I WILL find it. So the probability of finding an electron in all the space (integral of Ψ*Ψ dτ) is....??
ONE (1)
<Ψ|Ψ>=1
Beautiful
Amazing
Cheff kiss
I think? Im probably not wrong
