I started watching the video lecture series here: https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2016/video-lectures/part-1/ I notice that they use the term "operator" without first explaining it. Operators are also not explained (in fact they are not even mentioned) in my...
I absolutely agree, I'm disappointed in some sections of the book are only mentioned briefly without proper explanations and they would have needed more information.
I made some pictures of the related parts from the book, if it helps:
So what does only <x^2> represent?
I already answered, see post above. Unfortunately there isn't more information given in the example written there than what I've written here.
The question is not whether that answer is correct, which I already verified it is. The question is what the answer means. Does <x^2> represent the expected value for the potential energy of the particle in the box?
Thanks for a direct answer. Measurement of position makes sense, because the answer was L/2, which means the expected value for the position is in the center of the box which makes sense.
"Square of a measurement of position" however, seems more like a mathematical abstraction than representing...
I'm sure that's very good but I really just want to know some examples of what the functions represent physically.
Example: Find (a) ##<x>## and (b) ##<x^2>## for a particle in its ground state in a box of length L.
So I calculated these and got some values, and I checked the answers are...
The expectation value of any function ##f(x)## is given by <f(x)>= \int_{-\infty}^{\infty}f(x)\psi^2(x) dx
But what is ##f(x)## actually? In a physical sense.
For example if ##f(x)=x## or ##f(x)=x^2##, what do these functions represent on a physical level?
It is customary on other forums that the OP (original post(er)) decides the topic of the thread.
I wonder if the same custom applies here, because it seems this forum rather has a custom that says "if someone who has made a lot of posts on the forum doesn't like the topic being set by OT, they...
Actually in that question I was referring to a water molecule, and was considering whether a single water molecule could show wave characteristics or just particle characteristics?
Diffraction.