Electron/Photon locations 1) Is there any way that we can trace the path of an electron in an electron cloud (surrounding an atom). I know we can calculate the probability of an electron at any point, but can we actually map the path? 2) How 'localised' is a photon? Can we actually pin point the location of a photon?
The 'electron cloud' isn't a physically tangible object, and the idea of tracing a path is meaningless.
What do you mean by not a "tangible object." Well obviously we can't hold it, but we can't hold a lot of things yet we still can locate it.
The 'electron cloud' is just a way of picturing the probability distribution. It merely represents the squared modulus of the electron wavefunction. If we attempt to measure the position of the electron, this wavefunction instantly collapses and the electron appears to be somewhere in the 'electron cloud' with the associated probability. The electron wavefunction will then undergo unitary evolution as described by the Schrodinger Wave Equation, until we measure it again. As you can see, there is no concept of 'path'; it's not like the Bohr model where the electrons are flying round in circular orbits.
We can't calculate the probability to find an electron at a certain point,but only the probability density. Daniel.
Whereas with Newton's laws we have the position and momentum which are functions of time, in quantum mechanics, it is the wavefunction which evolves with respect to time. Now the wavefunction in position basis (which is basically a complex number for every point in space), when multiplied by it's conjugate and integrated (triply) between some limits will tell you the probabilty of finding it in that region of space. If you actually measure the position of the electron, it'll be found somewhere, as described by the wavefunction, but once you've measured it, the wavefunction will "jump" to become a wavefunction which describes the position of the electron of exactly where you just found it. However, as time goes on, the wavefunction will evolve as described by Schrodinger's equation.
The problem in asking and answering questions such as this is how does one defined a "path". Our typical inclination is to make a position measurement of an object over a period of time and thus, have a record of what that object is doing as a function of time. We can also trace the location of the object in space. But as has been mentioned, for quantum particles, as soon as one makes a measurement, a whole bunch of things change. However, does that mean we have no way at all to visualize an "orbital" so much so that we relegate it to an "abstraction"? I disagree and I certainly would not call it physically not tangible. The issue here is whether we CAN make an "orthorgonal" measurement in such a way that we do not collapse the position observable and thus, preserve the orbtals. Remember that if I make a measurement on an observable, the corresponding non-commuting observables remain undetermined (or uncollapsed). The infamous Schrodinger Cat-type experiments of Stony Brook/Delft did just that - preserving but observing the effect of superposition via another non-commuting observable. So can the same thing be done to observe atomic orbitals? YOU BETCHA! One can observe such things via looking at the reciprocal or momentum space. In fact, when you do an x-ray diffraction experiment, what you are directly probing is the momentum space of the material being studied. It is with this concept in mind that I say that orbitals are not physically intangible but have been observed directly. Using a combination of electron and x-ray diffraction techniques, Zuo et al.[1] have observed the textbook d orbital for Cu in a Cu-O bond. The real-space image shows directly the complex shape of the [tex]d_{z^2}[/tex] orbital as expected from QM! So this is not something intangible. The existence of atomic orbitals are as "real" as any other physical entity in physics. We just have to be a bit smarter in trying to observe such things. Zz. [1] J.M. Zuo et al., Nature v.401, p.49 (1999).
Well that's a cool result, hadn't come across that! I remember reading some stuff by Kip Thorn about 'going beyond Heisenburg' at LIGO by measuring in momentum space too... I'll try to get hold of that Nature papre.
1. A clear and simple no. There are no particle trajectories in qm. That's what qm is all about. Only waves and probabilities. 2. Yes (for example when it hits a plate). But the more precise you localize it, the less you know about where it's going. In the case of the plate you have practically no knowledge of where it's going afterwards.
is electron still particle in the electron cloud I accept and agree to James' views, but can we say that electron is still a particle in the electron cloud(which gices probability distribution),though we may not be able to accurately find its position.
Bohmian mechanics The answers I've seen so far on the thread are under the usual version / interpretation of quantum mechanics, the one I was taught. It turns out that there is an alternative version, usually called "Bohmian Mechanics", which treats the electrons as point objects with classical trajectories. Bohmian mechanics is quite old and is still being worked upon. Bohmian mechanics consists, in brief, of making Schroedinger's equation classical by assuming a special potential function, the "quantum potential". The wave functions then end up a result of insufficient information, rather than a part of reality per se. To learn more about Bohmian mechanics click these links: A survey from Arxiv: http://arxiv.org/abs/quant-ph/9504010 First few pages read okay in this introduction: http://arxiv.org/abs/quant-ph/0408113 416 more hits: http://www.google.com/search?hl=en&q=site:arxiv.org+bohmian+mechanics Carl