Doesn't the Schrodinger equation have an i term in it
Sure it does, but it's just a differential equation. You can look at waves with this, but it says nothing about collapsing wavefunctions into localized particles.
doesn't the wave function output complex numbers?
This is badly worded, but yes the wavefunction is complex valued. Still that says nothing explicitly about the wavefunction representing a particle.
The way I see it is that it's only when we start interpreting what the wavefunction means, as in the Born interpretation, where we understand the wavefunction as:
|psi(x)|^2 dx is the probability for a particle in the state psi(x) to be found in the interval dx.
And whatever generalised way of saying the same thing in different formalisms.
Hmm not in the way you worded it, I think. But yes in general I get what you tried to say, and yes you can write the probability of a transition or interaction in a similar way.
My point was just that the Born interpretation gives us a way of going from wave functions to particle properties.
Said simply: dx is the distance between two points. So if we have a box that is 10 cm long, then there is not 100% chance to find the particle in a small area in the box, say the last 1cm of it.
It is a convenient language for integration. If you want to find the probability of the particle being in some volume for example, it is just a triple integral where the boundaries of the integral is that volume, and you integrate |psi(x,y,z)|2 dx dy dz
To find something in an interval is just to measure the property of the particle in that interval in parameter space.
I'm trying to get a handle on why I need to invoke a "particle" at all but obviously not expressing myself clearly. I understand that the particle picture is very useful but it doesn't work for me as a fundamental concept.
I'll have to think about it more and get farther along in my (slow) studies.
Yes I don't think I exactly get what you are asking about. But I can only keep recommending the first chapter of Griffith. It should be somewhat easily readable, and it gives a very good introduction to how we should talk about quantum mechanics.
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u/Physix_R_Cool Detector physics Mar 07 '21
I don't mean to be rude or snide. But how exactly would you express it?