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

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

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