Recent content by sineontheline

This is interesting. So its not always true that V** = V (dual of the dual is the vector space I start with)? What's the intuition for why it's true for certain cases but not for others? What makes Hilbert Spaces so special? Do Fourier spaces have this property? Where can I find more...

So I'm pretty sure I understand the formalism of dual vector spaces. (E.g. there exist objects that operate on vectors and take them to scalars. these objects themselves form a linear vector space). But I'm having difficulty understanding where this comes from intuitively. How would I know...

*bump* :)

So I'm studying molecules and symmetry and I was wondering if there was a intuitive way of understanding why there are as many irreducible representations as there are classes. I keep getting lost in the math of the characters.

yo that was helpful thx.

So I'm trying to teach myself MO Theory and Spectroscopy. I was just wondering why symmetry was so important in understanding these and what characters are used to do. I know this is a broad question, but I've been reading a lot (Cotton, etc..) so I know they have to do with integrals and...

1. could anyone give sort of a qualititative explanation of how symmetry and irreducible representation are related in the context of molecular spectroscopy? like why is it so useful to count how many symmetries a molecule has and what does it have to do with irreducible represenations and...

okay so i was reading a book on representations and found this discussion and was confused: http://books.google.com/books?id=Hm-aKMkKXzEC&lpg=PP1&dq=group%20theory%20and%20physics&pg=PA53#v=onepage&q=&f=false it starts at the bottom of pg 53 and ends at the top of pg 54 so I understood the...

oh it wasn't that i didn't understand. its that he doesn't go into enough detail calculating the hydrogen ion. I looked up the orginal paper where it was derived. and when he starts talking about higher order bonds. i mean, i read it a while ago too. this is just what i just remember. but still...

I posted this elsewhere but I wasn't sure if physics people were lurking on the chem forum. I want to understand MO and LCAO. The chapters in Levine weren't enough. Are there other books on bonding that people know of?

Eugine and Fredick rock my socks. thx btw: I'm reading ballentine (ch 3) now...and understanding it! also Eugine: that discussion *really* helped

Why does unitarity of the representation of Lorentz/Gallile Group in Hilbert space imply that infinitesimal Lorentz/Gallile Transformations in space are generated by the Hilbert space's hermitian operators? I mean I know I've seen that exp(i*a*Lz) {'a' is parameter) generates the rotations...

Ha, okay. Basically what I'm thinking: The angular momentum operator (Lx, Ly, Lz) behave like the generators of SO(3) and SU(2) in that the lie algebras of SO(3) and SU(2) act like Lx, Ly, and Lz. And so because they're all homomorphic, rotation invariance of space expresses itself in QM...

"The idea that space is rotationally invariant is incorporated into QM as the assumption that there's a group homomorphism from SO(3) into the group of symmetries." This was the idea I was looking for. You go on to say that the representation of SO(3) isn't quite there though. So would it be...

As i understand it, the commutation rules for the quantum angular momentum operator in x, y, and z (e.g. Lz = x dy - ydx and all cyclic permutations) are the same as the lie algebras for O3 and SU2. I'm not entirely clear on what the implications of this are. So I can think of Lz as generating...