@radioactivered
really enjoy your posts and your take on rad. Perhaps you meant to say bremss from e is due to the atomic electrons that provide the repulsive force that the deflects this electron which then emits a photon due to conservation of energy. Tx, great account btw
NEWSOM: Fox News needs to keep paying the price until they change the way they do business. I just wanted a simple apology. Own up to your lies. They refused. They thought they would get this thrown out. And this judge said hold on boys and girls — lets get ready for discovery.
@macjshiggins And I am looking for an imaging sensor to complete the diagnostic. my university lab is funded by a us govt agency but r cash strapped, all people in my lab are usa citizens. where can i acquire a surplus lwir/mwir camera for this. if u dm me i can give u website to my lab. Tx
@macjshiggins Hello, i run a university lab in the southwest USA. My lab is focused on pulsed power driven high energy density physics plasmas. I want to image the instabilities from these sources and i want to field a phase contrast imaging diagnostic to do so. This pci uses a CO2 LASER.
i really cannot express enough how completely fucking baffled i am that people choose to live in places where there's a winter. you just have fucking *months* of the year where it's a freezing hell to go outside, where your skin dries and cracks and bleeds, where you have to constantly shovel snow and de-ice roads, where all the trees die and the animals hide, where the sun disappears and you're trapped inside in darkness again and again. and you just *live with it*
YOU CAN MOVE!!! NOT EVERYWHERE IS LIKE THIS!!! THIS IS NOT A FUNDAMENTAL FEATURE OF THE PLANET!!!!! THERE IS PLENTY OF SPACE!!!!! IF YOU LEAVE NOW YOUR CHILDREN WON'T BE TRAPPED INTO ACCEPTING AND NORMALIZING THE HELLSCAPE YOU RAISED THEM IN!!!!
Lecture 2 on our Quantum Mechanics Series
Schrödinger’s equation doesn’t start from mystery. It starts from a very specific bet…the state of a particle is a complex field ψ(x,t), and whatever dynamics we write down must move ψ forward in time in a way that preserves total probability.
We ask a basic question…what equation should ψ satisfy so that |ψ|² behaves like a conserved density, the way mass density does in fluid flow?
What is ψ?
Think of ψ(x,t) as the amplitude assigned to “the particle is at position x at time t”. It’s not a probability. It’s the object you add first, and only at the end do you square
p(x,t) = |ψ(x,t)|²
Because ψ is complex, it has magnitude and phase. Write it in polar form
ψ(x,t) = r(x,t) exp(i θ(x,t))
Then r² = |ψ|² is the density, and θ will end up controlling flow (the probability current).
Where does Schrödinger’s equation come from?
Start with two empirical inputs about waves and particles:
E = ħ ω
p = ħ k
Here ħ (“h-bar”) is Planck’s constant divided by 2π. It’s the unit conversion factor between the wave description (frequency ω, wavevector k) and the particle description (energy E, momentum p). In units, ħ has units of joule-seconds, so multiplying ω (1/seconds) gives energy (joules), and multiplying k (1/meters) gives momentum (kg·m/s). It’s the number that tells you how much energy or momentum you get per unit frequency or wavenumber.
A plane wave with angular frequency ω and wavevector k is
ψ(x,t) = A exp(i(k·x − ω t))
Now notice what derivatives do to this wave:
∂ψ/∂t = −i ω ψ
∇ψ = i k ψ
∇²ψ = −|k|² ψ
Multiply those identities by ħ:
i ħ ∂ψ/∂t = ħ ω ψ = E ψ
−i ħ ∇ψ = ħ k ψ = p ψ
−ħ² ∇²ψ = ħ² |k|² ψ = p² ψ
So for plane waves, the operators
Ê = i ħ ∂/∂t
p̂ = −i ħ ∇
act like energy and momentum!
Now use the classical nonrelativistic energy relation:
E = p²/(2m) + V(x)
This is bookkeeping for a particle moving slow enough that relativity can be ignored. The term p²/(2m) is kinetic energy. If p = mv, then p²/(2m) = (m²v²)/(2m) = (1/2)mv². The term V(x) is potential energy. It depends on position because forces come from spatially varying energy. A slope in V pushes the particle. Examples: for a charged particle in an electric potential φ(x), V(x) = q φ(x). Near Earth, V(z) = mgz. The point is total energy equals kinetic plus potential.
Turn that into an equation for ψ by replacing E and p with the operators above:
Ê ψ = (p̂²/(2m) + V) ψ
Compute p̂² = (−i ħ ∇)·(−i ħ ∇) = −ħ² ∇², so we get
i ħ ∂ψ/∂t = ( −ħ²/(2m) ∇² + V(x) ) ψ
That is the time-dependent Schrödinger equation.
The derivation here is a controlled heuristic: we matched the plane-wave identities to the measured relations E = ħω and p = ħk, then imposed the same energy bookkeeping as classical mechanics.
Why this equation is the right kind of rule
If ψ is the state, we need a rule that preserves total probability:
∫ |ψ(x,t)|² dx = 1
Schrödinger evolution does. You can see it by deriving a continuity equation.
Let ρ(x,t) = |ψ|² = ψ* ψ.
Take a time derivative:
∂ρ/∂t = ψ* ∂ψ/∂t + ψ ∂ψ*/∂t
Use Schrödinger and its complex conjugate:
∂ψ/∂t = (1/(i ħ)) ( −ħ²/(2m) ∇²ψ + Vψ )
∂ψ*/∂t = (−1/(i ħ)) ( −ħ²/(2m) ∇²ψ* + Vψ* )
Plug in. The V terms cancel exactly, and what remains can be rearranged into a divergence:
∂ρ/∂t + ∇·j = 0
where the probability current is
j = (ħ/(2mi)) ( ψ* ∇ψ − ψ ∇ψ* )
This is the best way to explain ehat ψ is: |ψ|² behaves like a conserved density, and the phase of ψ is what drives the current j.
So in this series, ψ isn’t a slogan. It’s the object whose modulus squared is the density, whose phase generates flow, and whose time evolution is fixed (up to V) by matching wave relations to energy bookkeeping:
i ħ ∂ψ/∂t = ( -ħ²/(2m) ∇² + V ) ψ
#QuantumMechanics#SchrodingerEquation#WaveFunction#BornRule#Physics#MathematicalPhysics
ICE surround judge's car threatening to smash windows—then detain his high school intern.
Agents handcuff teenager to arrest him—until judge fights loudly to demand they check ID to confirm they have wrong person.
Court security noticed masked men sneaking pictures of the boy
The LAPD shot a woman at point blank range with a rubber bullet all because she was asking to get to her home. She posed absolutely no threat.
This is what Trump’s America looks like.
243K Followers 170 FollowingShining a light on Washington. NOTUS is now The Washington Sun.
Metro coverage: @washsunmetro
Analysis, ideas and narratives: @washsunperspect
3.5M Followers 63 FollowingThe Official *NASA* Webb X account.
The world's most powerful space telescope. Launched: Dec. 25, 2021. First images revealed: July 12, 2022.
460K Followers 3K FollowingMy daughter Jaime was murdered in the Parkland school shooting. My life is dedicated to reducing gun violence and saving lives. All opinions are my own.
8K Followers 1K FollowingJust some #fella doing his bit to counter disinfo and support 🇺🇦 in their battle against evil. It’s that simple. #NAFO Volya Radio
61K Followers 47K FollowingDog lover Screaming into the abyss Failed Archaeologist now Failed Comedian Voted Best Content on X by my Mom & her friend 🇺🇸Tuck Frump🦅
137K Followers 298 FollowingI study and write (via the @RMetS) about snow-patches on UK hills. Self-confessed chionophile and author of 'The Vanishing Ice'.
133K Followers 471 Following20 ans, Lyon 🇫🇷, étudiant en Relations Internationales à Lille, cartes, analyses, suivi des conflits armés et de l'actualité internationale.
2K Followers 71 FollowingI design electronics, mechanical stuff, write a bit of firmware and software, and consult.
Also @spirit.re on Вluеskу and [email protected]
496K Followers 24K FollowingEx-GOP Congressman turned pro-democracy fighter.
Co-founder of PAXIS — built to protect immigrants.
🛡 When ICE knocks, we answer.
Help us launch 👇
18K Followers 912 FollowingArt Detective丨Book 'Hitler's Horses' (18 languages)丨'Art detective will forever be a cool job title.' (Dan Brown after my recovery of the 'Blood of Jesus')
182K Followers 3K FollowingJournalist debunking propaganda on Fox @JulietJeske #🟦 Newsletter/Podcast at Substack
https://t.co/cLRw4wUCoh
https://t.co/Mq9d1iEhCL
921K Followers 789 FollowingThe Countdown with Keith Olbermann Podcast is back Mondays, Thursdays - now with a choice of FLAVORS! The audio podcast PLUS full video episodes on YouTube
83K Followers 45 FollowingEuropean Space Agency astronaut, on board the ISS 🛰️ for #εpsilon.
#Crew12. ISS Expedition 74/75.
French air and space force helicopter 🚁 test pilot.
1K Followers 5 FollowingAdvancing scientific excellence by publishing influential results in fundamental, applied, and interdisciplinary physics across @apsphysics' journals.
39K Followers 267 FollowingWatchprosite: Watch Community - in-depth watch reviews & discussions and industry news on luxury wristwatches & high horology. Reporting since 2001.
4K Followers 395 FollowingJournaliste défense pour Air&Cosmos, fana des systèmes militaires (qui vole, roule, flotte,...), membre du Réseau Nucléaire et Stratégie - Nouvelle Génération
438K Followers 768 FollowingSenior Space Editor at Ars Technica. Likes rockets. Author of the best-selling book on the Falcon 9 and Dragon, REENTRY. https://t.co/5HYUhJzFHZ
45K Followers 699 FollowingBy the numbers, the world's most popular & influential wrist watch blog magazine; with watch reviews, collecting advice, and buying guides. Est. 2007
6K Followers 114 Followinghttps://t.co/2ZcVmi8YCe is an online magazine dedicated to mechanical watches, including some of the finest examples of haute horlogerie.
22K Followers 298 FollowingNews about: Ukraine, the French defence technological and industrial base, European security, and more. Not an official account/pas un compte officiel.