Question

Dirac, Bra-Ket notation

Answer 1

Form 1.5 is some Bra-Ket definitions

Answer 2

In Leonard Susskind 's QM Lecture 1 at 1:02:52
he introduces vectors spaces
http://www.youtube.com/results?search_type=videos&search_query=stanford+theoretical+minimum+susskind&search_sort=video_date_uploaded

Answer 3

@Frostbite

Answer 4

The \(\large \delta_{jk}\) most be the Kronecker delta? in the attachment?

Answer 5

yes

Answer 6

\[\langle i|j\rangle=\delta_{ij}=\begin{cases}1&i=j\\0&i\neq j\end{cases}\]

Answer 7

does that describe the vector space

Answer 8

i think they also some times use \(\delta_{ij}=\delta_i^j\) notation

Answer 9

Alright. Well it sure makes sense, I better watch that video. Thank you.

Answer 10

So let me see if I'm just half or totally lost:
If we use normalized wavefunctions as I like to do, and should write it using Dirac notation I get that:
\[\Large \int\limits_{}^{} \Psi _{n}^{*} \Psi _{m} d \tau=\langle n |m \rangle\]

Answer 11

yeah i think so

Answer 12

Hmmm what do I do with my lovely operators \(\large \hat{\Omega}\)?
I suppose they belong in the middle?
\[\Large \int\limits_{}^{}\Psi _{n}^{*} \hat{\Omega} \Psi _{m} d \tau=\langle n|\hat{\Omega}|m \rangle\]
It seems a little confusing to me :)

Answer 13

i am not familiar with \(\hat\Omega\)

Answer 14

I just wanted Omega to be any observable and the hat that it is a operator.

Answer 15

for probability to be true, the limits of the integral of the wave function over -∞ to ∞ must =1

Answer 16

the ket is a dual vector psace, isnt it?

Answer 17

if ket corresponds to a state whose function is given by \(\psi\), and bra-B, is representaed by a state state \(\phi\) then the state of the system, such as hudrogen, then the relationship is the scalar product \(\int \phi *\psi d\tau\) .

idk that's what i read in my notes. Lol.

Answer 18

I just remember doing bra-ket using linear algebra. matrices, and so forth.

Answer 19

@nincompoop ?

Answer 20

@abb0t if you got any additional material I would be very happy, I'm kinda the one who asked UnkleRhaukus if he had any material on it.