Recent content by hunc

Thanks! It was my first attempt, which never really got carried out. I thought ##\nabla^2\phi## can bring in ##1/\hbar^2## and ##\partial_t \phi## only ##1/\hbar##... And I just go through it and all is fine. And now I kind of want to ask what's the story about the wiki and the equation $$...

Homework Statement I am reading Mathematical Concepts of Quantum Mechanics (Stephen J. Gustafson, Israel Michael Sigal. Second edition). The book would like to find an evolution equation which would lead to the Hamilton-Jacobi equation $$\frac{\partial S}{\partial t}=-h(x, \nabla S) $$ in the...

I'll try to do that today.

Thanks so much! This idea came up earlier today. But I didn't find it plausible. For if x << dm, then we get to keep the linearity, but A then must be suffiently small. Note that it takes quite some distance to reach 100e-10 A. One the other hand, if x is only somewhat smaller than dm, then...

The distance between the photon emitter (the bulb) and the electron emitter (the metal). But strictly speaking, both of them have protective coverings. So I was really measuring the distance between them. (There are arrows supposed to imply the exact position of the real emitters.)

Homework Statement I am doing the photoelectric effect experiment. And we were trying to verify the relationship between photoelectric current and distance is I \times d^2 = k, where k is a constant.(At least I believe this to be true.) But from the data, I kind of get a I= k d^{-2} + b . And...

I'll check it out. Thanks for the input.

Thanks still.

Maybe I didn't put it clear enough. A 4D space is what I had in mind before reading Arnold. But in the book Mathematical Methods of Classical Mechanics, it introduce galilean space-time structure as a affine space A4. And it kind of offers the difference between the two case in the image. What...

Before t=0, we have an affine space. By t=0, we fixed a point in "time", not "space". So how should we end up with a linear space?

I dig into a Lie group textbook and find the definition. Thanks.

I see. I guess I'll have to wait for the special relativity to come in. I still don't get it. How does "t=0" provide a fixed origin for the space (if that is indeed what it takes to change a affine space to a linear space)? Regards, hunc

I just start to read Mathematical Methods of Classical Mechanics by Arnold. And I am sort of very puzzled by all the notion. Firstly, if the universe is seen as a 4D affine space, why is time a mapping from R^4→R? I mean this kind of 4D contains time, right? Secondly, I thought the kernel of...