The Random, Meaningless Announcements Thread 3!

[Polymath257]

Might summon @Polymath257 to tell me definitively (if I don’t hear back from classmates on Slack) if a notation for quantum operators and eigenbases (eigenbasises?) from my book is the same thing as from a problem I’m working on, because of all the things to trip me up, a stupid notation difference between authors is the most annoying

Edit: I need to just write exp[i f(A)] in Dirac notation, A is a Hermitian operator whose values are known

Edit 2: derp is it legal to expand the exp as a series in Dirac notation? Did I mention I hate Dirac notation and it’s been years since undergrad QM, or linear algebra for that matter? I need to sleep.

These are my dumb notes, which don’t render well on a phone.

Yes. Also, the eigenvalues of exp(iA) will be of the form exp(ia) where a is an eigenvalue for A.

Technically, you need to worry about things like convergence, but physicists tend not to do so. As long as there is a good spectral decomposition of A, it will work (even if A is not a bounded operator).

Yes, bra-ket notation is just one of those cultural things mathematicians have to deal with when talking to physicists.

Here's a joke (from the math side):

How does a physicist tell when a series converges? Ans: the terms go to 0.

How does a quantum physicist tell a series converges? Ans: the second term is smaller than the first.

 

[Wu Wei]

I'm going to put drops in my eyes

 

[Wu Wei]

just a note.....teaching or spreading false history for political gain is a dangerous path

 

[ChristineM]

just a note.....teaching or spreading false history for political gain is a dangerous path

Never stops politicians

 

[PoetPhilosopher]

Never stops politicians

Or radio personalities and TV evangelists

 

[sun rise]

The sun is shining.
The farmer's market is beckoning.
Why am I typing this?
Good point, I'm out of here for the nonce.

 

[Polymath257]

Humans don't deserve dogs.

 

[Revoltingest]

Campbell's manhattan clam chowder for breakfast.

 

[Shadow Wolf]

Humans don't deserve dogs.

They really are better than we are.

 

[sun rise]

eigenvalues

Now that does take me back to the far distant past. For those like me who have utterly and totally forgotten what they are:

Eigenvalues are a special set of scalars associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic roots, characteristic values (Hoffman and Kunze 1971), proper values, or latent roots (Marcus and Minc 1988, p. 144).

The determination of the eigenvalues and eigenvectors of a system is extremely important in physics and engineering, where it is equivalent to matrix diagonalization and arises in such common applications as stability analysis, the physics of rotating bodies, and small oscillations of vibrating systems, to name only a few. Each eigenvalue is paired with a corresponding so-called eigenvector (or, in general, a corresponding right eigenvector and a corresponding left eigenvector; there is no analogous distinction between left and right for eigenvalues).

The decomposition of a square matrix

into eigenvalues and eigenvectors is known in this work as eigen decomposition, and the fact that this decomposition is always possible as long as the matrix consisting of the eigenvectors of

is square is known as the eigen decomposition theorem.

Eigenvalue -- from Wolfram MathWorld

 

[Stevicus]

A coffin that was found in a golf course pond contains a 4,000-year-old man buried with an axe (msn.com)

 

[Revoltingest]

They really are better than we are.

Speak for yourself, toots.

 

[Shadow Wolf]

Speak for yourself, toots.

I have yet to be harmed by a dog.
People, on the other hand, they've gave me plenty of reasons to be suspicious and on alert around them, to unhealthy and self defeating ends.

 

[Revoltingest]

I have yet to be harmed by a dog.
People, on the other hand, they've gave me plenty of reasons to be suspicious and on alert around them, to unhealthy and self defeating ends.

I've never had a problem of people crapping in my yard.
And I've never had a person bite me.

 

[Shadow Wolf]

I've never had a problem of people crapping in my yard.
And I've never had a person bite me.

I was bitten by a kid once when I was a kid.
And if a dog craps on my yard it's a human's fault for not cleaning up, dumping animals off, over breeding, and demand for pure breeds.

 

[Revoltingest]

I was bitten by a kid once when I was a kid.
And if a dog craps on my yard it's a human's fault for not cleaning up, dumping animals off, over breeding, and demand for pure breeds.

Canine apologist!
Humans invented...
- Bacon
- Superheterodyne tuning
- Wrenches
- Cartoons

 

[Shadow Wolf]

Canine apologist! Cynical misanthropic pessimist

Fixed it.

 

[Revoltingest]

Fixed it.

Humans are more useful than dogs.
No dog invented The Red Death or the BLT.

 

[Stevicus]

 

[Shadow Wolf]

Humans are more useful than dogs.
No dog invented The Red Death or the BLT.

Dogs didn't invent those. Nor did they invent torture, bombs, amd they don't act in cruelty and spite.