Recent content by JonnyMaddox

Ok thank you. Ok another question. You can map a four vector to a 2x2 complex matrix like this: X= \begin{pmatrix} x^{0}+x^{3} & x^{1}-ix^{2} \\ x^{1}+ix^{2} & x^{0}-x^{3} \end{pmatrix} while det(X) =(x^{0})^{2}-(x^{i})^{2} Is the Lorentz invariant distance, which means that every...

I'm currently reading a book on relativistic field theory and I'm trying to understand spinors. After the author introduces the four parts of the Lorentz group he talks about spinors and group representations: "...With this concept we see that the 2x2 unimodular matrices A discussed in the...

Ok thank you, that sounds nice. I'm trying to understand it. So what is the geometric interpretation? But next, what about spheres and tori? I think if I fully understood this I could put it up on Wikipedia as a generalisation of the binomic formula.

Hey JO, You all know the binomic formulas I guess. Let's look at the first: (a+b)^2=a^2+2ab+b^2 Now this can be interpretet as the area of a square with the sides (a+b). And that means the area of the square is decomposed into the components a^2,2ab and b^2. And this can also be done for a cube...

Hey JO. The Hamiltonian is: H= \frac{p_{x}^{2}+p_{y}^{2}}{2m} In quantum Mechanics: \hat{H}=-\frac{\hbar^{2}}{2m}(\frac{\partial^{2}}{\partial x^{2}}+\frac{\partial^{2}}{\partial x^{2}}) In polar coordinates: \hat{H}=-\frac{\hbar^{2}}{2m}( \frac{\partial^{2}}{\partial r^{2}}+\frac{1}{r}...

Hi thanks, I'll look that up. I use maxima anyway.

Hi, I'm looking for a program that spits out fully summed index equations. For example T_{ii} in, out comes T_{11}+T_{22}+... and so on, with Einstein summation convention.

Ok I think I'm confused about what q^{I} and p_{J} are. Coordinates and conjugate momentum ok. But are they the basis of the space or what? If not how does this make sense \hat{G_{i}}= q^{1}(G_{1})_{1}^{1}p_{1}+...? So it's just a number or what?

Ok I see. Now I understood this: A_{ij}|e_{i}><e_{j}|= A_{11}|e_{1}><e_{1}|+A_{21}|e_{2}><e_{1}|+A_{12}|e_{1}><e_{2}|+A_{22}|e_{2}><e_{2}|=A_{11}\begin{pmatrix} 1 & 0 \\ 0 & 0 \end{pmatrix}+A_{21}\begin{pmatrix} 0 & 0 \\ 1 & 0 \end{pmatrix}+A_{12}\begin{pmatrix} 0 & 1 \\ 0 & 0...

Another good method is the following: Type the name of the concept you don't understand (math or physics) into Google like this "appropriate name of math concept or words that make sense in that context pdf". Then open up every pdf you find as tab (if you know two or more languages you can do...

BTW: Ok one book that I think is very straight forward is Paul Dirac's Book The Principles of Quantum Mechnics ! It's short and good in coordinate free notation, he even introduces a bit of quantum field theory, but it is a little outdated on that, but that doesn't do much to the whole book. And...

And this is why?

Sry but that's not answer to my question.

Ok thanks Sam. Could you also help me with coordinate representations? How do I apply this formula \hat{G_{i}}=q^{I}(G_{i})_{I}^{J}p_{j} Is this like an inner product of the coordinates and the conjugate momentum? Like this \hat{G_{1}}=q^{1}(G_{1})_{1}^{1}p_{1}+q^{2}(G_{1})_{2}^{2}p_{2}+...

Screw textbooks. Either watch the lectures by Leonard Susskind. Or look for pdfs on Google, search for something like "Introduction to QM" pdf or similar words.