Previously, Niels Bohr explained the levels in an atom. When Louis de Broglie suggested that they might also be both wave and particle, things made more sense: there were discrete energy levels in atoms. In simple terms, it describes what electrons do under almost any circumstances. To do so, one needs to insert a term that describes the situation—the V. If it gets close to an atom nucleus, V will have a different formula. The mathematical side is beyond the scope of this article, but the results fall right within the boundaries of our interest.
Initially, it shows how complex the atom orbitals are, with their varying shapes as either spheres or the shape of dumbbells. This is a transcript from the video series Understanding the Misconceptions of Science. Watch it now, on Wondrium. However, the focus here is on psi, which equals the square root of Pi times e to the minus r, where r is related to the distance from the center of the atom. For example, if the equation is used for a hydrogen atom, many things about it can be predicted: the radius of the atom and the wavelengths of light that hydrogen emits.
What psi shows is actually the potential place where the electron could be. Psi is biggest at the center of the atom, i. Librarians Authors Referees Media Students. Login Become a Member Contact Us. Follow Us. Breeding a Better Robot.
Programmable Materials. Physicists Look at Animal Behavior. What Makes a Physicist? Members in the Media. This Month in Physics History. Education Corner. This result is now known as Heisenberg's uncertainty principle and it's one of the results that's often quoted to illustrate the weirdness of quantum mechanics.
It means that in quantum mechanics we simply cannot talk about the location or the trajectory of a particle. In other words, all you can expect from the mathematical representation of a quantum state, from the wave function, is that it gives you a probability. Whether or not the wave function has any physical interpretation was and still is a touchy question. For them the wave function was only a tool for computing probabilities. Why should we believe this rather fantastical set-up?
The famous physicist Richard Feynman considered this a futile question: "Where did we get that [equation] from?
It's not possible to derive it from anything you know. Yet, the equation has held its own in every experiment so far. According to Ernest Rutherford's atomic model, the frequency of radiation emitted by atoms such as hydrogen should vary continuously.
Experiments showed, however, that it doesn't: the hydrogen atom only emits radiation at certain frequencies, there is a jump when the frequency changes. This discovery flew in the face of conventional wisdom, which endorsed a maxim set out by the 17th century philosopher and mathematician Gottfried Leibniz : "nature does not make jumps".
In Niels Bohr came up with a new atomic model in which electrons are restricted to certain energy levels. We will also explore another weird consequence of the equation called quantum tunneling. Marianne Freiberger is Editor of Plus. She interviewed Bouatta in Cambridge in May I am semi-retired, so I have the time now to learn those subjects I should have taken in high school, and college. This is just for my own curiosity, and to exercise my brain.
Thanks for this article. I found it very interesting. Was just browsing the web looking for a quick blurb about schrodinger and found this. Very nice setup and nice flow. Reminded me of my college days.
Thank you very much for this very nice illustration, developed step by step chronically. Reading this nice article, one can see how quantum mechanics evolves and understand it better. Thank you very much. A very concise article giving a big picture description of the basic tenets of QM. Would have been more impactful if the article was written straight instead of writing quotes from the interview.
Although I am a PhD student in physics and have been studying quantum physics for several years, this article gives me a better view and summary of quantum concepts. With special thanks. Thanks Marianne.
I was looking for a straight forward explanation of Schrodinger's equation, and here is your thoughtful article. The best article on schrodinger's equation ever read. Helped me a lot. Good job. Thanks for the nice article. I just notice that the solution of the Schrodinger equation in the special case is a function of time whereas it should be a function of space only.
This is by far the best description I've ever seen on Quantum Mechanics and the Schrodinger Equation. Simply brilliant Professor Dave! It's the first of your series I've watched and it most definitely gives me a reason to subscribe and watch more. Trying to help my daughter studying and understanding some physic I stumbled across this fantastic and superclear article! In an eye-blink I refreshed all my 35 years old knowledge!
But none of these approaches provides a satisfying explanation for one of the defining features of quantum mechanics: its linearity. This linearity gives quantum mechanics some of its uniquely non-classical characteristics, such as the superposition of states. Some of the choices resulted in a stronger coupling between the wave's amplitude and phase in comparison with the coupling in the classical equation. In quantum mechanics, both amplitude and phase depend on each other, and this makes the quantum wave equation linear.
Because this coupling between amplitude and phase ensures the linearity of the equation, it is essentially what defines a quantum wave; for classical waves, the phase determines the amplitude but not vice versa, and so the wave equation is nonlinear.
For example, we can't have right and left running waves adding to get standing waves because of this nonlinear term. It's when we have standing waves left and right running wave solutions that we most naturally get the eigenvalue solutions which we must, like the hydrogen atom eigenstates. So emphasizing linearity is very important. In the past, physicists have debated whether the imaginary unit—which does not appear in classical equations—is a characteristic feature of quantum mechanics or whether it serves another purpose.
The results here suggest that the imaginary unit is not a characteristic quantum feature but is just a useful tool for combining two real equations into a single complex equation. In the future, the physicists plan to extend their approach—which currently addresses single particles—to the phenomenon of entanglement, which involves multiple particles.
There are lots of fun things that one can consider and we are trying to fit these together and see where each of these perspectives takes us. It is also fun to find out who has had ideas like this in the past and how all the ideas fit together to give us a deeper understanding of quantum mechanics. If our paper stimulates interest in this problem, it will have served its purpose. Copyright Phys. This material may not be published, broadcast, rewritten or redistributed in whole or part without the express written permission of Phys.
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