He did such a wonderful job of then deriving the hydrogen atom wave function and much more.
"How you get the right equation, is less important than getting it. "Schrödinger was breaking new ground and did the heroic job of getting the right equation," Scully said. In this way, the authors of the current paper are building on Schrödinger's own revolutionary discovery. Scully added that understanding the history of both the science and the scientists involved can help in providing a deeper appreciation of the subject. It's too bad that we don't spend more time motivating and teaching a little bit of history to our students but we don't and, as a consequence, many students don't know about the origins." And if you put this into a Hamiltonian for the classical dynamics of particles, you get the Schrödinger equation.
"We are often taught (see, for example, the classic book by Leonard Schiff, 'Quantum Mechanics') that energy is to be replaced by a time derivative and that momentum is to be replaced by a spatial derivative. "Many physicists, maybe even most physicists, do not even think about the origins of the Schrödinger equation in the same sense that Schrödinger did," Scully told. Scully, a physics professor at Texas A&M University, explains how physicists may use the Schrödinger equation throughout their careers, but many still lack a deeper understanding of the equation. Instead, they often simply postulate the classical-to-quantum rules….The reason given is that 'it works.'"Ĭoauthor Marlan O. In the case of quantum mechanics, there are so many convincing experimental results that many of the major textbooks do not really motivate the subject. Usually, many bubbling brooks and streams merge suddenly to form a mighty river. Often, it is difficult to locate uniquely its spring despite the fact that signs may officially mark its beginning. "The birth of the time-dependent Schrödinger equation was perhaps not unlike the birth of a river. In the new study, the scientists have shown that it's possible to obtain the Schrödinger equation from a simple mathematical identity, and found that the mathematics involved may help answer some of the fundamental questions regarding this important equation.Īlthough much of the paper involves complex mathematical equations, the physicists describe the question of the Schrödinger equation's origins in a poetic way: Schleich, et al., from institutions in Germany and the US, explain that physicists usually reach the Schrödinger equation using a mathematical recipe. In a new paper published in PNAS, Wolfgang P.