Anyone familiar with Dirac's quantum notation?

[Semtex]

I missed 3 weeks of class, went in, and was completely baffled for 2 hours. I think the operator is outside the ket, the eigenvalue is in the ket, and I have no idea whats in the bra, possibly the complex conjugate of the eigenvalue. Bra's and kets together is the dot product of the two. Am I anywhere close?

[m_the0ry]

Essentially you are right. Bras are row vectors and kets are column vectors, so a bra-ket is a scalar (dot) product, and a ket-bra is a tensor (matrix) product. Bra is the complex conjugate of the ket for any given symbol.

Not confident enough to answer the question in more detail - i don't know where eigenvalues come in - myself but Wikipedia does a pretty good job:

http://en.wikipedia.org/wiki/Dirac_notation

[yukoncpa]

Wasn't it Dirac who came up with the notion of Anti-matter? I've enjoyed laymen's books about him, such as, "In Search of Schroedenger's Cat"
Can't really help you, but maybe try this link: link (http://en.wikipedia.org/wiki/Bra-ket_notation)

I'm sure you've tried this already. Sorry, I can't be of more assistance.

[cambraceres]

Ket is just the representation of the abstract vector. The operator is outside of, but still acts upon Ket. Bra is the Hermitian conjugate, or conjugate transpose of ket.

This notation yeilds an inner product, defined on complex hilbert space.

Just study it, like alot.

Cam

[Semtex]

[ QUOTE ]
Essentially you are right. Bras are row vectors and kets are column vectors, so a bra-ket is a scalar (dot) product, and a ket-bra is a tensor (matrix) product. Bra is the complex conjugate of the ket for any given symbol.

Not confident enough to answer the question in more detail - i don't know where eigenvalues come in - myself but Wikipedia does a pretty good job:

http://en.wikipedia.org/wiki/Dirac_notation

[/ QUOTE ]
i read the wiki article and it was as confusing as the book. It doesn't help that the book was written by the professor and is completely meant to be a sidenote to the lectures. I understand things somewhat except where the eigenvalues and eigenstates come in to the picture, plus when you start adding terms to the middle and around. Like what does it mean when you have a ket leading a bra in a term, instead of the other way around?

[Metric]

Dirac notation is the only way to fly...

"x" eigenstates: |x>

"p" eigenstates: |p>

Arbitrary state vector: |Psi>

Hermitian conjugate of |Psi>: <Psi|

Now, note that "1" can be written as: Sum_x |x><x| (or you can use any other complete orthonormal basis)

Now, the function Psi(x) = <x|Psi> and it's Fourier transform is Psi(p) = <p|Psi>

Inner product between Psi(x) and Phi(x) = <Phi|Psi> = Sum_x <Phi|x><x|Psi> = Sum_x Phi^*(x) Psi(x) = Sum_p <Phi|p><p|Psi> = Sum_p Phi^*(p) Psi(p)
(this is how you get back and forth between your ordinary "function notation")

An operator can now be decomposed into a particular basis very easily. For example, the operator X = sum_x x |x><x| (where x is the eigenvalue). Now if you want to, say, find the expectation value of X with respect to state Phi, we have the expression <Phi|X|Phi> = <Phi|sum_x x |x><x|Phi> = sum_x x <Phi|x><x|Phi> = sum_x x Phi^*(x)Phi(x) -- similarly for any other basis.

The notation is so efficient that it keeps you straight sometimes when you've lost touch with physical intuition and rules for how things are supposed to work -- a subtly incorrect expression is often OBVIOUSLY incorrect when you express it in Dirac notation, and there's only one way things can "look right."

[Borodog]

Bra-ket notation is teh hotness.