Anybody have some fun books/movies to recommend? Just got done with a shoulder surgery and i suddenly have a lot of downtime. bonus points if it's science related but doesnt have to be.
Try reading Geometry Of quantum Theory or Gravitation Textbook by Charles W. Misner and Kip Thorne... It'll surely be a good pass time you won't forget rest of your life...
@JohnRennie Have you tried Charles W Misner? :P
Only thing I hate in Computer Science engineering is that, the more you read, the more newer things come out... you might have completed a textbook with 10 k citations and when you surf internet, there are 50 other textbooks with 10 k citations.
There's one with non linear programming, dynamic programming, integer programming, all, one better than other...
Even if I take my whole life, I'd barely touch the essence of Computer Science Engineering Mastery....
@RewCie John is recovering from shoulder surgery, and you're recommending MTW? That book's so heavy it can be dangerous for even a healthy person to lift it! ;)
Can I pick up quantum field theory after Shankar's Principles of QM, or would I need to study more QM?
Anyone else find the notation $|\Omega V\rangle$, $\langle \Omega V|$ confusing? This notation breaks the equal preference between bras and kets. Because of this notation, bras have to be understood in terms of the corresponding ket
Is there any reason why we've stuck with this notation?
@BioPhysicist @BioPhysicist I thought about that function inner product. We could interpret (af,g) as the function af of the bra-function space, multiplied by the function g of the ket-function space. To evaluate this, we would flip the order of these functions in the product. To do that, we convert the bra af to the corresponding ket a^* f, and g to the corresponding bra g. So, we get: (af,g)=(g,a^* f)^*=a^**(g,f)^*=a(f,g)
But if we define the inner product, not as the product of two vectors of the same space, but as simply the matrix multi of a bra with a ket, then we can have it linear in both components. The property (a,b)=(b,a)^* would become bra(a)ket(b)=(bra(b)ket(a))^*, where bras and kets would obey bra(a)=adjoint(ket(a))
by bra(a), i mean a vector <A|. Similarly for the ket
we can use the property bra(A)ket(B)=(bra(B)ket(A))^*, and the linearity in the second component, to prove the linearity in the first component
I proved it for the inner product of functions above
An inner product takes two vectors from the same vector space and outputs a number
whatever you define via the application of a "bra" to a "ket" is not an inner product
You cannot define the inner product of $\lvert \psi\rangle$ and $\lvert \phi\rangle$ as $\langle \phi\vert \psi\rangle$, because the definition of the map from ket $\lvert \phi\rangle$ to bra $\langle \phi\rvert$ requires the inner product
Hello everyone. Any hints in showing that $\int_V \rho \vec{u}\cdot \nabla \vec{u}\,\text{d}V$ is a force if $\vec{u}$ is acceleration and $\rho$ is density?
given an inner product that's linear in the first argument, the bra corresponding to a ket $\lvert \psi\rangle$ is defined by $\langle \psi\vert \phi\rangle := (\lvert\phi\rangle,\lvert\psi\rangle)$
@ACuriousMind Yea, it's impossible. Even proving the existence of orhthonormal basis uses the definition of inner product. So a basis-independent definition is a must here
I spent half of my day thinking whether the inner product properties were implied by bra-kets or the other way around lol.
