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to explain a wide range of phenomena involving electrons, atoms, and light. After a great deal of effort, a new theory (together with a new law of motion) emerged in 1924. That theory is known as quantum mechanics, and it is now the basic framework for understanding atomic, nuclear, and subnuclear physics, as well as condensed-matter
There are many good reasons to address the hydrogen atom beyond its historical signiflcance. Though hydrogen spectra motivated much of the early quantum theory, research involving the hydrogen remains at the cutting edge of science and technology.
We have seen that both the Schrödinger and the Heisenberg equation follows from Von Neumann’s Hilbert space formalism of quantum mechanics. Consequently, we have proved that this formalism properly unifies both Schrödingers wave mechanics, and Heisenberg, Born, and Jordans matrix mechanics.
The solution to this equation will be individual functions \(\psi(\vec{r})\), each corresponding to a different allowed state, each with a corresponding energy level. The solutions that represent an atom— where the electron is bound to the proton— have \(E<0\).
Schrödinger’s version of quantum mechanics is based on the evolution of a wave function characterizing the system, a notion previously introduced in Chapter 4, as dictated by the Schrödinger wave equation. This is the approach we will take here. It is interesting to
The Schrödinger equation is the heart of non-relativistic quantum me-chanics, in that virtually all the physics is derived from its solutions in var-ious systems. The origin of the equation is difficult to pin down, as every book on introductory quantum mechanics has its own way of introducing it.
29 lis 2021 · Working essentially independently, in the mid-1920's Heisenberg and Schrödinger both created a full form of Quantum Mechanics. How these two extraordinary events occurred has been extensively studied; a favorite reference is Max Jammer, The Conceptual Development of Quantum Mechanics (McGraw-Hill 1966).
