The Dirac equation emerged from multiple simultaneous contributions in 1928, with Kramers' independent work and modern derivations from Ehrenfest relations and hydrodynamics now detailed.
Takabayasi, On the formulation of quantum mechanics associated with classical pictures, Prog
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The Schrödinger equation is derived assuming the wave function is a probability amplitude and using the de Broglie relations E = ħω and p = ħk for the associated wave.
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The Birth of Quantum Mechanics and the Dirac Equation
The Dirac equation emerged from multiple simultaneous contributions in 1928, with Kramers' independent work and modern derivations from Ehrenfest relations and hydrodynamics now detailed.
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Derivation of the Schrodinger equation from fundamental principles
The Schrödinger equation is derived assuming the wave function is a probability amplitude and using the de Broglie relations E = ħω and p = ħk for the associated wave.