Schrödinger picture example: quantum harmonic oscillator by Ciro Santilli 35 Updated 2025-01-29 +Created 1970-01-01
TODO: use the results from the quantum harmonic oscillator solution to precisely illustrate the discussion at Schrödinger picture with a concrete example.
- something about finding a unitary representation of the poincare group
- why the square: physics.stackexchange.com/questions/535/why-does-kinetic-energy-increase-quadratically-not-linearly-with-speed on Physics Stack Exchange. Ron Maimon's answer is great, as it relies only on the following staring points:He also offers a symmetry argument considering the case of potential energy.
- why the half: physics.stackexchange.com/questions/27847/why-is-there-a-frac-1-2-in-frac-1-2-mv2 on Physics Stack Exchange
It is so mind blowing that people believed in this theory. How can you think that, when you turn on a lamp and then you see? Obviously, the lamp must be emitting something!!!
Then comes along this epic 2002 paper: pubmed.ncbi.nlm.nih.gov/12094435/ "Fundamentally misunderstanding visual perception. Adults' belief in visual emissions". TODO review methods...
Dirac equation vs quantum electrodynamics by Ciro Santilli 35 Updated 2025-01-29 +Created 1970-01-01
TODO: in high level terms, why is QED more general than just solving the Dirac equation, and therefore explaining quantum electrodynamics experiments?
Also, is it just a bunch of differential equation (like the Dirac equation itself), or does it have some other more complicated mathematical formulation, as seems to be the case? Why do we need something more complicated than
Advanced quantum mechanics by Freeman Dyson (1951) mentions:
A Relativistic Quantum Theory of a Finite Number of Particles is Impossible.
Bibliography:
- physics.stackexchange.com/questions/101307/dirac-equation-in-qft-vs-relativistic-qm
- physics.stackexchange.com/questions/44188/what-is-the-relativistic-particle-in-a-box/44309#44309 says:
By several reasons explained in textbooks, the Dirac equation is not a valid wavefunction equation. You can solve it and find solutions, but those solutions cannot be interpreted as wavefunctions for a particle
- physics.stackexchange.com/questions/64206/why-is-the-dirac-equation-not-used-for-calculations
- www.physicsforums.com/threads/is-diracs-equation-still-useful-after-qed-is-developed.663994/
Adds up chemical energy and kinetic energy.
Wikipedia mentions however that the kinetic energy is often negligible, even for gases.
The sum is of interest when thinking about reactions because chemical reactions can change the number of molecules involved, and therefore the pressure.
To predict if a reaction is spontaneous or not, negative enthalpy is not enough, we must also consider entropy via Gibbs free energy.
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