Recent content by Technon

So operators are just functions

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.

<x^2> represents expected value of the potential energy and it has been calculated to be not zero, then that seems incorrect.

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?

Ok. The answer for that question was 0.283L^2. Does that mean that this is 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?

Use latex code when writing equations.

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.

There exists arguments based on logic, you know.

You asked for just one example, and you confirmed I listed two examples.