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. Whether the cat in the box can also be considered an observer in quantum mechanics currently remains unclear.In a new paper published in PNAS, Wolfgang P. But a measurement made to determine the state that the particle is in destroys the interference patterns and gives rise to different behavior that seems more like that of tiny particles hence the phenomenon of wave-particle duality.
Under the laws of quantum mechanics, electrons, photons, and all other particles are each in a number of superposed states that interact with each other, forming interference patterns, and giving rise to an overall behavior that often seems wavelike. This thought experiment provides an extreme case of the condition in which small-scale objects always exist. It is neither alive nor dead, or it is both alive and dead, depending on how you want to look at it. In other words, without being observed, the cat does not exist in a particular state at all. The act of observation changes that, and one state becomes established to the exclusion of the other. In quantum-mechanical terms they are in a condition of superposition. But until the observation is made, the two possible states, which are mutually exclusive, coexist.
Thus, after an hour, there is equal probability of the cat being alive or dead, and an observer can open the box and see which state the cat is in. If an alpha particle is emitted and hits the Geiger counter, a relay is set in motion whereby the hammer shatters the flask, releasing the gas and killing the cat. Over the course of an hour, there is a chance that the radioactive substance might emit an alpha particle, and an equal chance that it might not. Schrödinger would have us imagine a cat inside a closed box with a tiny bit of a radioactive substance and an apparatus consisting of a Geiger counter, hammer, and flask of cyanide. The indeterminacy can be resolved by observation but entails a paradox. It shows how quantum-mechanical indeterminacy at a microscopic level can cause indeterminacy at a macroscopic level. A Closer Look Schrödinger's cat is a thought experiment proposed by the physicist and philosopher Erwin Schrödinger.