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The Dirac equation which is the equation for describing the wavelike behavior of electrons. It predicted the existence of antimatter and particle spin. You st

The Dirac equation which is the equation for describing the wavelike behavior of electrons. It predicted the existence of antimatter and particle spin. You start with the Schrödinger equation, add relativity to get the Klein-Gordon equation which is a mess because it's second order in time involving negative probabilities, if you in ways "take the square root" of it you get the Dirac equation. Relativity has been part of the understanding of electrons since 1928. https://en.wikipedia.org/wiki/Dirac_equation https://en.wikipedia.org/wiki/Dirac_equation

colechristensen 3mo ago
To add to this, this "square root" operation done to derive the Dirac equation is where spinors i.e. electron spin i.e. the Pauli exclusion principle i.e. the reason atoms exist at all comes from. Likewise antimatter. The "second order in time" of the Klein-Gordon equation comes from adding relativity and the "fix" reducing that to first order time is the source of antimatter and spin. So yes very much so relativistic effects are a foundational part of QM.
alok-g 3mo ago
Thanks for the insights. I am interested in learning all this stuff. Am currently going through just Schrodinger's Equation. Do you have book recommendation(s) that include insights everywhere just like what you shared? Thanks.
- colechristensen 3mo ago
  These are books to train physicists, accessable-ish to a math heavy engineering undergraduate degree holder. The insights above are my own and extractable from this material but not necessarily stated out loud (unless I'm unconsciously plagiarizing which is entirely possible) * David Griffiths - Introduction to Elementary Particles * Chris Quigg - Gauge Theories of the Strong, Weak, and Electromagnetic Interactions And the wonderful Richard Behiel's videos on YouTube https://www.youtube.com/watch?v=8Iu74b5iCuQ https://www.youtube.com/watch?v=8Iu74b5iCuQ
  - alok-g 3mo ago
    Thanks a lot. Have been watching these videos all day long! Looked through the first book too.

colechristensen 3mo ago

To add to this, this "square root" operation done to derive the Dirac equation is where spinors i.e. electron spin i.e. the Pauli exclusion principle i.e. the reason atoms exist at all comes from. Likewise antimatter. The "second order in time" of the Klein-Gordon equation comes from adding relativity and the "fix" reducing that to first order time is the source of antimatter and spin. So yes very much so relativistic effects are a foundational part of QM.

alok-g 3mo ago

Thanks for the insights. I am interested in learning all this stuff. Am currently going through just Schrodinger's Equation. Do you have book recommendation(s) that include insights everywhere just like what you shared? Thanks.

colechristensen 3mo ago
These are books to train physicists, accessable-ish to a math heavy engineering undergraduate degree holder. The insights above are my own and extractable from this material but not necessarily stated out loud (unless I'm unconsciously plagiarizing which is entirely possible) * David Griffiths - Introduction to Elementary Particles * Chris Quigg - Gauge Theories of the Strong, Weak, and Electromagnetic Interactions And the wonderful Richard Behiel's videos on YouTube https://www.youtube.com/watch?v=8Iu74b5iCuQ https://www.youtube.com/watch?v=8Iu74b5iCuQ
- alok-g 3mo ago
  Thanks a lot. Have been watching these videos all day long! Looked through the first book too.