Quantum Mechanics: Particle-Wave Duality

[cam875]

so does quantum mechanics state that all particles can be represented by waves and that it is needed to do so in order to describe some of the crazy things observed at the atomic and subatomic level.

 

[mathman]

so does quantum mechanics state that all particles can be represented by waves and that it is needed to do so in order to describe some of the crazy things observed at the atomic and subatomic level.

You got it right essentially. It also means radiation has particle properties as well.

 

[cam875]

so which state on its own is better at explaining our universe? a wave or a particle because it seems like a wave might be.

 

[AzonicZeniths]

so which state on its own is better at explaining our universe? a wave or a particle because it seems like a wave might be.

It depends which aspect of our universe you think about. If you are thinking subatomic, or atomic it would be waves, but in the larger sense, it would be particles.

 

[cam875]

ok makes sense, thanks for the info.

 

[AzonicZeniths]

ok makes sense, thanks for the info.

No problem :). But, I guess I should include that there are actual molecules that can act as waves when experimented with, mainly in the double slit experiment. So, I guess what I'm getting at is that stuff doesn't have to be subatomic or atomic (I believe molecules are slightly bigger than the term 'atomic'...er...mabey) to have both wave and particle properties.

 

[cam875]

ok, In chemistry we've always been taught about electrons in nice fixed orbits around the nucleus of an atom. But i keep reading how there actually in a cloud formation around the nucleus and that there like waves and stuff. Can u give me a little explanation on how 2 electrons around a nucleus for helium can create this cloud?

 

[AzonicZeniths]

Well, electrons are not in fixed orbits, electrons, rather, appear and disappear in flashes. This 'cloud' is also metaphorical. The electron 'cloud' is an area of space that the electron has the highest probability to appear in. This probability can be tied to the uncertainty principle, which I highly recommend you read up on; just wiki it :P

 

[cam875]

yes I have been reading up on it for a little bit now. I don't understand what they mean when they talk about how the environment itself influences the electrons to certain areas. Do they mean by us touching them in order to measure them? Also are electrons always moving very fast?

 

[AzonicZeniths]

how the environment itself influences the electrons to certain areas

I did not fully understand what you meant by that, maybe site would help me out. But, I think you may be talking about the observer effect.

And yes, electrons always move very fast, but, from what I have read, it is differentiable.

 

[Demystifier]

so does quantum mechanics state that all particles can be represented by waves and that it is needed to do so in order to describe some of the crazy things observed at the atomic and subatomic level.

I suggest you to read Sec. 2 of the pedagogic review
http://xxx.lanl.gov/abs/quant-ph/0609163 [Found. Phys. 37 (2007) 1563]

 

[DeShark]

so does quantum mechanics state that all particles can be represented by waves and that it is needed to do so in order to describe some of the crazy things observed at the atomic and subatomic level.

Wave-particle duality is... well it's helpful at the start, but becomes confusing if you don't get what it's there for.

In ye olde dayse of physics, somewhere around the turn of the 20th century, physics was founded upon Newton's mechanics, (which had the abstract idea of particle) and maxwell's electromagnetism (which had the abstract idea of wave/field). So in order to classify a system, the entities in the system had to be either particles (like billiard balls) or waves... So when things like electromagnetic radiation began to behave like particles (photoelectric effect) and vice versa, it confused the hell out of the folk back then. Hence this wave particle duality.

They concluded that the theory of the time was wrong. Neither Newtonian mechanics nor maxwell's equations could be correct. So they decided to create a physical description based solely upon what was observable. Thus the new theory contained neither waves nor particles. But it did give the right results. Which was the most important thing. I prefer to think of electrons and protons and all the other "elementary particles" as particles. This was Feynman's approach. When they are detected, they are completely detected. You never find half an electron or a third of an up quark. However, these particles are said to be in certain physical states.

There are two main representations of these states: the schroedinger picture, in which the states are represented as wave functions; the Heisenberg picture in which the states are vectors in a mathematical Hilbert space. In the schroedinger picture, it just so happens that the square of the amplitude of the wave function (cause they can be complex) is the same as the probability density function for finding the particle at a given point.

I hope this has cleared things up rather than made it more confused. Essentially, wave-particle duality is an old notion, based on the fact that everything is either a wave or a particle. In actuality, everything is described acurately by QM and thus these abstract notions of waves and particles are largely unnecessary. As Feynman said "shut up and calculate".

 

[cam875]

lol "shut up and calculate" so is the wave function used to find out the probability of an electron being in a certain location or am i still a little confused. And can u use vectors to contruct how the electrons move and stuff around the nucleus, an image might help me understand here.

 

[Zizy]

About vectors - this is only different formalism of the same thing... It is impossible to perfectly predict trajectory of an electron, if you meant that with construction how electron moves.
As for orbitals - these are just energy states... an electron can exist in states in between, but these are unstable and the electon will sooner or later go to the lower state. (pauli's principle makes sure that all electrons don't fall to the ground state, Heisenberg's makes sure they do not fall to the core)

 

[cam875]

I see so ur saying that there's more orbits than we think in an atom?

 

[enotstrebor]

Wave-particle duality is... well it's helpful at the start, but becomes confusing if you don't get what it's there for... As Feynman said "shut up and calculate".

The first law of logic (Aristotle) states that something is either A or not A.

There can only be a wave particle unity.
[if of couse one believes in a reality outside oneself].

The term wave-particle duality is because, as indicated by Schrodinger and still true today ``to combine both into a unified formulation has not been possible'' [not verbatim].

Thus wave-particle duality covers over this inability of the present theory (...confusing if you don't get what it's there for).

So don't be confused.

 

[DeShark]

lol "shut up and calculate" so is the wave function used to find out the probability of an electron being in a certain location or am i still a little confused. And can u use vectors to contruct how the electrons move and stuff around the nucleus, an image might help me understand here.

The wave function (or state vector, same thing) contains all the information that can be found via measurement. One of these observable things is the position of the particle. Thus the wave function can tell you the *probability* of a particle being found in a certain location as you say. However, I would not advise you to have a mental picture of electrons spinning in orbits around the nucleus. What is useful is a picture of so-called electron clouds. I hate the term "cloud" as it implies that the electron itself is spread out through space around the nucleus. I think of the cloud more as the probability of finding the electron in that area of space - the probability density in 3 dimensions. To help you visualise these "clouds" or density functions, I just found a good page at http://www.falstad.com/qmatom/

It let's you change n, the energy of the atom, l, the total orbital angular momentum, m, the projection of the angular mometum along a given axis. Remember that these clouds are the probability density functions for finding the electron in that position around the nucleus. That is to say you are more likely to find an atom near the nucleus when it has a lower energy.

What a lot of people tend to get confused between is graphs of energy levels and their mind's picture of electron orbits and distances from the nucleus. Remember that a quantum leap is a leap between energy levels. It's the energy of the electron that leaps, not the electron itself.

Try not to think about electrons "moving" in the nucleus. This is one of the great failures/successes of Quantum mechanics. It only predicts things that one can actually measure. It doesn't give a picture behind what's going on. This was Einstein's pet peeve about QM. It also let's you know how the things you want to measure will progress in time. Feynman gives a very nice introduction to the subject in his 3rd volume. It's truly an amazingly clear read. I can't recommend it enough. I can't do it justice. Buy the book and enjoy!

 

[cam875]

so in some cases its better to represent something as a particle and sometimes a wave? it just depends on the cirumstances? Also does working with waves require more math or to use more complex math?

 

[DeShark]

so in some cases its better to represent something as a particle and sometimes a wave? it just depends on the cirumstances? Also does working with waves require more math or to use more complex math?

It's always better to treat things according to quantum mechanics. There are no waves and no particles in the traditional sense in quantum mechanics. However, just as Newtonian mechanics works well in a low velocity limit, so does a particle viewpoint if the wavelength of the particle is much less than other typical lengthscales.

So for experiments involving electrons, where the typical length scale is in the range of nano meters, you can often just ignore the fact that the electron has wavelike properties. However, photons of red light will interfere and show other wavelike effects. Both these things (photons and electrons) are called particles, but this is really quite confusing. There are two types of particle. Those of the old days when matter was made up of particles and those of quantum mechanics which are described by the wave mechanics of Schroedinger.

Please get a book and read up on the topic if it interests you. Reading stuff on the internet will likely confuse tremendously. As will media science like Scientific American. Knowing something about complex numbers and vectors is likely very necessary. I'd recommend Feynman's 3rd volume...

Failing that, check out the Douglas Robb Memorial lectures:http://www.vega.org.uk/video/subseries/8

They're aimed at general members of the public who don't know anything about maths hardly. It depends what your maths competence is like as to which you'll prefer... They'll both clear it up!

 

[richard14]

I have a question guys am a beginner in physics excuse my ignorance, but my question is
can pair creation be done with two high energy photons collision or does it need a nucleus
to absorb energy and momentum, i ave seen these two theories which one is the correct.

 

[cam875]

ok thanks for all the info, ill probably look at those lectures.