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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
He wrote down a wave equation (the so-called Schrodinger equation) that governs how the waves evolve in space and time. We’ll deal with this equation in depth below. Even though the equation is correct, the correct interpretation of what the wave actually meant was still missing. Initially Schrodinger thought (incorrectly) that the wave
Heisenberg, with help from Max Born and Pascual Jordan, came up with a matrix theory, which supposedly explained the travels of the electron by a complex form of mathematics called matrices. There remained some problems, however.
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 .
After Schrödinger had shown the mathematical equivalence of wave mechanics, which he had discovered, with quantum mechanics, the fruitful combination of these two different areas of physical ideas resulted in an extraordinary broadening and enrich-ment of the formalism of the quantum theory.
The Schrodinger equation: “norm”, “one particle” Important concept: the norm associates ψ(x,t) with “one particle” The association of “one particle” is associated with the “norm” of ψ(x,t). We require that ψ(x,t) be normalized so that: 1 = Z +∞ −∞ dxψ∗(x,t)ψ(x,t) . (5.31)
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.
