Introduction to Dirac Notation

In this video, I give examples of the types of vectors in Hilbert Space, and I introduce Dirac Notation.

Questions? Let me know in the comments!

ADDENDUM: the part in the end with the inner product should be rewritten as psi|psi = integral |f(r,t)|^2, not just |f(r,t)|^2 as I mistakenly put in the video.

[swinThoughtSeize]

"which like most forum posts devolved into an argument between a couple of angry neckbeards"

I came here to learn, but the laugh is appreciated haha. Great serie so far, very condensed and to the point !

[swavekbu]

This is why understanding linear algebra is SO important. It's the basis (no pun intended!) of so much more.

[wernerheisenberg]

Really nice, thank you! Your videos are helping me a lot to get through quantum mechanics :)

Btw. it's "Bra-c-ket"
c for "column" for the vertical line ;)

[thomasbissinger]

Hi there,
Sorry, I just wrote a lengthy comment about how the <psi|psi> part in the end is wrong, but I saw you already put it as an addendum. (Can you maybe put it in the video as well? Easily overlooked if its at the end of the description. Or at least put it first in the description.)
So just one tinier thing: saying that the state |psi> is represented by a time-dependent function is also somewhat imprecise. One should rather say that a time-dependent state |psi(t)> or |psi>(t) is represented by a time-dependent function f(r, t). The state space in nonrelativistic quantum mechanics has no time-dependence.

[jackvernian]

Thank you, dirac notation as explained in griffiths was a bit too confusing, your video nailed it!

[picobarco]

Hi when someone below said : Bra== " it may be called a conjugate ket". From Linear Algebra there is a term called Dual Space, the Bra-Vector Space is the Dual Space of the Ket-Vector Space. I hope this will clear up the issues surrounding the relationship between Bra and Ket spaces. Hilbert spaces in Quantum Mechanics, is not the general Hilbert Space, it is a specific subset of Hilbert Space referred to as a "Rigged Hilbert Space".

[davidwright]

Please NUMBER the videos in order! Makes them easier to find, and makes sure nothing's\beeen ignored/lost. Thanks.

[pamelaadams]

This is very good. Thanks for the clear explanations and statements.

[maxyang]

This is extremely concise and helpful. Thank you

[bowmanryan]

It's most likely a little flare from paulie boy bra-ket goes to bracket for the angled brackets being in its complete form.

[estanislaomarquez]

Hi. I really like you videos. But I think that the inner product represented by bracket is the integral of the square of the module. Please, let me know if I am wrong. Greetings!

[safdaransari]

please provide more videos on quantum mechanics.

[iotaphysics]

which book should i follow with yours lectures?

[tenorsaxophone]

Here's a thought: <ψ|ψ> is referred to as a bracket (brah-ket)
So shouldn't <ψ| be pronounced as "brah" like in bracket instead of "braw" as in the undergarment?

[OmnipotentEntity]

In my QM class, the professor pronounced bra as you are pronouncing it in this video.

[nilspaz]

It Is pronounced BRA as the undergarment that women wear and the pronounciation does not change when it is together witha Ket. This was the pronouciation Dirac used anf i heard him many times at FSU

[motilaljana]

it may be called" conjugate ket"

[Graham_Wideman]

1:00 "within an orbital, an electron can be either spin up or spin down". Ok, so that's a single variable, with two possible values -- ie: a single boolean value. Why do we need a vector with two entries, each of which is real?

[frede]

There's something that's not clear to me, and I would be very thankful if someone could help me. So as he talks about in the video, the wave function can be expressed in various ways using ket vectors, for example as a spin state or a "spinor", or as a position wave function. Now, the wave function itself is an abstract vector, and the position wave function psi(x) is just the components of this vector if you are in position space or position basis. The same vector can also be expressed in some other basis, such as in a momentum basis, in which case the components will be a function Ø(p), which is just the same as the Fourier transform of the position wave function. However, they both describe the same abstract ket vector, the vector is just expressed in different bases. The problem is that the ket vector used to describe spin is clearly not the same as the one used to express psi(x) or Ø(p), and in fact, they must exist in different Hilbert spaces. My question is what is the relationship between these two different ket vectors, both frequently used to describe the state of a particle?

[urieldaboamorte]

why is it that you don't need to take the transpose of the function? supposing it'll be represented by a matrix since we're talking about vectors. thanks!