The physics of atoms and molecules as the essence of modern physics was born from Schrödinger's wave equation for the Hydrogen atom in 1926. Let me cite from Epistemology and Probability, Bohr, Heisenberg, Schrödinger and the Nature of Quantum Theoretical Thinking by A Plotnitsky:
- Schrödinger’s wave mechanics aimed at offering, and initially appeared to be able to offer, a theory that would be realist and causal and thus would conform to the "classical ideal".
- It was expected to be able, just as classical mechanics did, both to describe the physical processes at a subatomic level (as wave-like processes) and to predict, on the basis of this description, the outcomes of the experiments involving these processes.
- While Schrödinger’s hopes concerning the descriptive capacity of his theory did not materialize, on the predictive side the theory was spectacularly successful.
- Schrödinger’s equation does not describe any physical waves, as Schrödinger initially hoped it would. Instead, quantum probabilistic predictions—enabled by Born’s rules for deriving probabilities from quantum amplitudes.
Schrödinger did not change his philosophy. Instead, he came to doubt and even to repudiate quantum mechanics, at least as a desirable way of doing physics, although he acknowledged that the theory and even understanding it in ‘‘the spirit of Copenhagen’’ (which remained philosophically deplorable to him) may have been imposed on us by nature itself.
We understand that Schrödinger from start was searching for mathematical model within classical continuum mechanics as a wave equation describing the mechanics of an atom, including radiation spectrum. The Schrödinger equation for a Hydrogen atom with one electron has this form. Schrödinger never gave up his hope that his model somehow could be generalised to atoms with many electrons within the same frame of classical physics, with thus atom mechanics as a form of macroscopic mechanics just on a smaller scale.
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