Lmst

New video by Physics Explained! Always fun with great explanations, an entertaining watch. In a comment under the vid, a valid caveat by "physicsboy787" about why the gravitation analogy fails, which is sadly not mentioned in the video.

https://www.youtube.com/watch?v=0tGiwd_Zs00

#physics #quantumMechanics #waveEquation #hydrogenAtom #nielsBohr #wernerHeisenberg

Screenshot from the linked video showing two graphs and accompanying equations of the discrete and continuous momentum distribution of the electron in a hydrogen atom.

Youtube comment by "physicsboy787" under the linked video:

Your explanation of the question at the beginning of the video misses an important point that I think you should address.
There is no problem with the fact that the potential energy causes the electron to be attracted to the proton. That is easily solved by the electron moving on a circular or elliptical orbit like a planet around a star. In fact, the potential energy of the proton and electron is identical in form to the potential energy in Newtonian gravity. And we don't need quantum mechanics to explain why the Earth doesn't collapse into the Sun.
The real reason why we expect the electron to fall into the proton is because accelerating charges emit radiation. In order to orbit the proton, the electron must be accelerating and thus emitting radiation. But this radiation results in significant energy loss so we would expect the electron to spiral into the proton as it radiates away all of its energy. This is where quantum mechanics comes in to fix the problem, by requiring electrons to only be observed in orbits of fixed energy (known as orbitals) as you showed near the end of the video.
Otherwise, great introductory explanation of quantum mechanics. Love watching your videos!

Time-dependent and time-independent Schrödinger equations:
\[i\hbar\dfrac{\partial}{\partial t} \Psi(x,t) = - \dfrac{\hbar^2}{2m}\dfrac{\partial^2\Psi(x,t)}{\partial x^2} + V(x,t)\Psi(x,t)\qquad\text{(time-dependent)}\]
\[-\dfrac{\hbar^2}{2m}\dfrac{\partial^2\Psi(x)}{\partial x^2}+V(x)\Psi(x)=E\Psi(x)\qquad\text{(time-independent)}\]

#SchrödingerEquation #Schrödinger #WaveEquation #TimeDependent #TimeIndependent

by guest: #vvvv #waveequation why is the show&tell broken?

in many ways, #mathematical #physics is based on the #smoothing properties of the #integral

#integrableSystems #mathematicalPhysics #complexAnalysis #spectralTheory #harmonicAnalysis #functionalAnalysis #mathematicalAnalysis #differentialEquations #ODEs #PDEs #SDEs #DEs #equations #BrownianMotion #LangevinDynamics #dynamics #Langevin #StochasticDifferentialEquations #StochasticProcesses #WienerProcess #OrnsteinUhlenbeck #HarmonicOscillator #WaveEquation #Newton #Newtonian #Maxwell #Einstein

Our ears perceive only in a certain window of #Sound frequencies
Our eyes perceive only in a certain #Window of #Electromagnetic radiation frecuencies.
Outside of these we use devices to measure the two aforementioned.
Eqs of Theory Of General Relativity led to #WaveEquation. There were attempts to detect gravitational waves many years ago without success, so their detection now implies nothing but GRT predicts things that are eventually detected.

#WaveEquation

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