#schrodingerequation — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #schrodingerequation, aggregated by home.social.
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A Pendulum for the Multiverse: David Albert, Hugh Everett, and the Worlds We Never Feel
On my grandfather's porch in North Loup, Nebraska, the ground kept its promises. Summer evenings the floorboards held the day's heat, the corn stood in rows that ran clear to the horizon, and nothing in all that flat immensity so much as trembled. When a teacher first told me the Earth was spinning at close to a thousand miles an hour while racing around the Sun at sixty-seven thousand more, I pressed my bare feet against those boards and waited to feel the ride. The stillness came back like a verdict. Whatever the books claimed, my soles reported a stationary world, and a boy trusts his soles. Every child who has run that experiment has rebuilt, in miniature, the strongest objection the seventeenth century could throw at Copernicus. If the Earth turns, why does a dropped stone land at the foot of the tower and never a few feet to the west? Why does the gale of our orbital speed fail to strip the leaves from the trees? The objection deserved respect because it rested on evidence, on the honest testimony of every human body that had ever stood still. It took Galileo's ship, and then Newton's laws, to explain why that testimony, though honest, was worthless. […] -
In the past few weeks I have been trying to understand the eigenvalue problem (time-independent Schrödinger equation)
–𝑢'' + λ (cos 𝑥 + cos τ𝑥) 𝑢 = 𝐸𝑢
where λ is a parameter, 𝐸 is the eigenvalue (blame the physicists for the notation), τ is the golden ratio and the problem is posed on the infinite line. The motivation comes from quasicrystals.
Some solutions are localized around a minimum of the potential, but the none of the corresponding eigenvalues are isolated.
At higher energies, solutions spread out over the whole line, giving rise to the absolutely continuous spectrum which is a Cantor set.
This is wild, at least for me, but partially supported by my own computations and functional analysis results. But I am not fully confident of the former and struggling to understand the latter, so I am not sure whether this picture is complete or even correct.
The more I look into it, the less I understand ... any pointers are appreciated.
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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
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#GregoryChaitin - Is #Information #Fundamental?
https://www.youtube.com/watch?v=ByJe3abjDZo&ab_channel=CloserToTruth
#Philosophy #Science #PhilosophyOfScience #Metaphysics #Idealism #Matter #Probability #QM #QuantumMechanics #SchrodingerEquation #Numbers #Math #Maths #Mathematics #Computers #Computation #Universe #Theory #CloserToTruth #RobertKuhn
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The True Meaning Of The #Schrödinger #Equation
- Is the #SchrodingerEquation really a #Wave Equation? Or is it something else entirely?
https://www.youtube.com/watch?v=LFC2HsT6Bh4&ab_channel=TheScienceAsylum
#Science #Physics #Math #Maths #Mathematics #WaveMathematics #QuantumMechanics #QuantumPhysics #QM #SchrödingerEquation #Schrodinger #Newton #Acceleration #RestoringForce #Equilibrium #HeatDissipation #HarmonicOscillator #Heat #HeatEquation #Probability