Wavefunction and Wigner phase-space distribution for a quantum harmonic oscillator. It just rotates at constant speed, as with classical mechanics
But for non-quadratic potential, such as pendulum type dynamics, the distribution spreads out and generates interference patterns
hadn't really appreciated that the cross term is doing this, until I looked more closely at the visualization
The visualization is interesting
Superposition of 2 gaussians has oscillating cross term. Cancels if you integrate along X or P direction
joint x-p direction, parallel to the troughs, cross term won't cancel
Instead it cancels with the gaussians to give diffraction pattern for X-P
in quantum physics position X and momentum P canβt be simultaneously measured.
But, linear combinations aX+bP π’π³π¦ observable, and their distributions can be used to back out the joint X,P probability density.
The Wigner distribution
but, it is πΈπ¦πͺπ³π₯
β’ gamma function
β’ Wigner quasiprobabilities
β’ fractional Fourier transforms
β’ Mistakes in probability (historical)
β’ Itoβs lemma
β’ Randomness in number theory
β’ clickbait math, actually surprisingly interesting
β’ probability doesnβt exist!
which YT vid you want to see next?
bsky.app/profile/almo...
New YouTube video posted
βThe Joy of Couplingβ
Happy Valentineβs Day!
youtu.be/rpW2ZYtXn6o?...
YouTube video coming up tomorrow, on my channel, especially for Valentineβs Day!
βThe Joy of Couplingβ
watch this spaceβ¦
just invented perpetual motion
I remember doing this stuff before. The coupon collectors problem. Could compute exactly and approximate, or approximate using a Poisson process from the start.
something something Gumbel something
Youβre probably familiar with Fourier transforms. But, did you know that it can be viewed as a 90Β° rotation in the time-frequency domain and we can rotate by any angle via fractional Fourier transform.
Explains why applying FT twice gives reflection (rotation by 180Β°).
The Producers by Mel Brooks
Inaugural Board of Peace meeting is under way
Hey US-Americans, can you just give Trump Alaska? He wonβt know the difference and might keep him quiet for a bit
βagain! again!β
OTOH, if things have gone wrong, and you have to use the slide, is it bad form to ask for another go?
βdo you even lift bro?β
#QOTD
βI never said even a fraction of the shit thatβs ascribed to meβ
β π΄πππππ‘ πΈπππ π‘πππ
that was sister sledge
Woke up to this sight
hey everyone!
I won the knowbell prize!
Kids are really cute when theyβre at that age where they havenβt yet worked out that giving you their snack means less for them
Just cross off the last digit and take twice the last digit from whatβs left
butβ¦I usually combine with ad hoc techniques. Likeβ¦oh the number ends in 3, so add 7 and cross off the final 0.
never mind, was just responding but it went away so I posted anyway. obvs a silly reply but you answered my question
hey @johnbull.wtf you canβt just post this and delete it!
A second hand yacht? Really? How poor do they think we are?
so how hard are these ErdΓΆs problems anyway?
Land line
analogue tape
analogue clock
real life
it would be interesting to check exactly what happens if you do fractional FT to your two functions, then multiply and transform back. I expect convolution combined with a complex exponential exp(iaxy)
