Recent content by Prologue

The highest power of x in the force equation will have bound solutions if the power is odd (and the coefficient out front is negative). If the highest power of x is even, you will have the potential to have bound solutions at low energy (around the origin), but once you get to high enough energy...

Thanks for this thread, it has helped me out more than a few times.

Jackson suits a certain type of student very well. If you have a good, careful, thorough professor, like to read a book thoroughly (~20hours a week) and then straight up copy the methods out of the book when you are solving the exercises, you will do fine. If you are a more 'intuitive' person...

Unless you are using crazy units it is not del dot E = 4*pi*rho, it is del dot E = rho/epsilon zero. TO be honest, I am not quite sure what the question is. When you go to two dimension you can think of it as just x and y, so the z component is zero. That should pretty much answer your questions...

If there is no air resistance and you throw the ball up with a certain velocity, it stops turns around and comes back down, what will be the velocity as it passes by the spot you threw it from?

Any number that is a multiple of ten is even and divisible by 2. Then any number (base ten) denoted by ...dcba (where a is the ones place, b in the tens, etc.) will be divisible by two if a is divisible by 2 because ...+d*10^3+c*10^2+b*10^1+a represents the number and division is linear. All...

Try looking at it in this way...Remember the following rules: A row of a matrix can have all of its entries be multiplied by a number. The effect that this has on the determinant of this matrix is that the determinant gets multiplied by the number. If you do this on all rows of the matrix...

Yeah, that is basically what I am doing, trying to get a good viewpoint before I start grad work. I'll try to give it a more theoretical read-through and worry about specific details later. Thanks for the help so far. Also, what other books would you recommended?

The thing that is really bothering me is the change in the type of quantity on each side of the equals sign. We start out basically by saying the D's are matrices, fine good! But then we use an identical looking relationship except that some of the D's are 'turned' into vectors. And when you...

Well, that is different! He never said in the book that we didn't want stretches or reflections. However, he does say 'Take the group elements themselves to be orthonormal basis vectors for a vector space...' but that doesn't really clue me into what the D(g_{1}) in...

Why did he say "the dimension of a representation is the dimension of the space on which it acts"? I would say that it 'exists' in 1 dimension, but what is it acting on? I suppose, if elements of a representation only act on other elements of the same representation, then D(a)[D(b)] would be...

Is there an errata for this book (2nd edition)? I am wondering about some of the things that are stated just in the first few pages. For instance, he says "This is Z_{3}, the cyclic group of order 3." then stuff about defining a representation and then "the dimension of a representation is the...

In my opinion, your collection of degrees is a huge hindrance. It shows at the very least a lack of the ability to realize an incorrect course, then correct it. At worst it shows that physics is yet another fleeting thought for you. You want to be a physicist but never got an undergrad physics...

If you are no good at algebra (and live in the US) go to your local community college and for a couple hundred bucks you can get a 16 week course that you can ask all of your questions in. IF you don't know calculus, go enroll in Calc 1, then Calc 2, then Calc 3 and then Differential equations...

I buy that (and that was what I was thinking intuitively). I see that the path length difference per angular displacement will be more for a thicker object and that would explain the thin bands.