studiot

Actually you need this both of these to substitute into your general solution if you want to discount say H (w) or G(w). There is nothing wrong with the constant function, even if the constant is zero G(x-vt) = 0 for all x is perfectly OK (and twice differentiable) You are correct about the tan function and the reciprocal of the tan. The last one is, of course, a square wave if w is integral. Is this a wave or not in your eyes? I'm probably not putting this very well but for example a single atom of copper is not a conductor of electricity, but an array of them is.

I just posted this in another thread and it occured to me that I more often use a comma after 'because' than before it.

pmb Sorry that was my fault for not using x as the dummy variable. Replace x by w, with w=(x-vt) The question about restrictions is not a trick question. The partial wave equation and tour general solution only works for one case - that of an infinite wave in an infinite medium. All other cases introduce boundary condition restrictions to limit the choice of arbitrary functions. Our objective is to end up with only one choice. Further the choice of arbitrary funtion is not unlimited, they are at least bounded continuous functions, at least twice differentiable. I added my remark because, just as many forget the boundary conditions limit the choice of solution function as above, many treat the quantum mechanics of real matter as though it was just an assemblage of particles. This, of course, is not the case. As soon as you go to molecules you loose the identity of each particle and create a new structure. When you get as far as metals and semiconductors even more happens and you get effects that are impossible for single isolated particles. So tan (w) is disallowed because, although periodic, it regularly goes off to infinity.

'Cats Paws and Catapaults' ,Steven Vogel 'Chemical Binding and Structure', J E Spice Might interest you.

Sorry for the earlier misreading I thought you had said one-dimensional analysis, which is about high school pure maths. Never mind there are several disciplines that call soemthing plain dimensional analysis. Physics calls Lagrangian Mechanics this but you will need advanced calculus as the subject is pretty advanced mathematically. Physics also has a subject about units of measurement called simensional analysis which is to do with putting physical quantities like force and energy in terms of 5 basic dimensions which are mass, length, time, electric charge and temperature. This is not really applicable to atomic and sub atomic physics and therefore electrons. Chemistry and Pharmacy also uses this for keeping units correct http://www.chem.tamu.edu/class/fyp/mathrev/mr-da.html The first thing to establish is which form of dimensional analysis you are interested in.

So would you call any of these a wave? G = 0 G = constant G = tan(x) G = 1/tan(x) G = {1 : x odd, :x : even} I fully agree with this but there is more. All this quantum mechanics stuff that has been mentioned so far has been single isolated particle stuff. How many single isolated particles do you know? As soon as we get to real materials we are into molecular QM and the original particles loose their identity.

Pete, Thank you for discussing properly. What restrictions would you place on G or H ?

I don't disagree - But it is not a question of known experiment. We have not succeeded in dividing these particles. But that does not answer the question is there a single particle that carries sharge or spin or colour or mass or whatever any more than saying we have never observed a magnetic monopole proves they do not exist.

Juanrga, thank you for your interest. Dalton could equally have claimed all experiments to date show atoms to be indivisible, as could Rutherford and Chadwick claim about nuclear particles. My desire to have a one to one correspondence between a property and a carrier particle has not been assuaged, although I am looking into severin's details.

Pete, I said periodicity is fundamental to wave behaviour and have pointed out some uses of the word periodic that do not conform to your 'definition'. Brillouin zones are periodic in space. The periodic table is periodic in atomic number. There are indeed other structures which are periodic but are not waves. However I still maintain all waves are periodic. Back to waves, have you ever heard of the 'periodic equation' for a wave? You can write these for any wave (as far as I know). Sometimes they can be quite complicated, especially if there is a dispersion term in the original PDF as with Schrodinger. Incidentally adding a dispersion term can lead to the solitary waves I mentioned earlier with appropriate boundary conditions. Coulson does a fair job of deriving these periodic equations for many wave types in his book Waves.

I didn't describe a theory I described a real world practical situation. I can actually observe, measure and display the wavelike behaviour. The behaviour is incontrovertibly there and real. It is not 'derived from any theory'. The nodes and antinodes of the wave are not parts of a quantum waveform, but they exist. The question is like asking 'why do I not see a standing voltage waveform between my house and the power station?' One is a wave theory that offers this for the real periodic variation in voltage that I observe and measure. The other is a theory of particles that, as far as I know, should lead to a different solution that of no periodic waveform, rather a constant voltage or constantly decreasing voltage with the only variations due to random motion of those particles. If you think that taking a container of light (but not zero) weight plastic balls and blowing them down a tube can lead to a periodic distibution of balls I would be glad to read you mathematical derivation.

Before you can do one dimensional analysis for your purpose or most others you will need some algebra and some trigonometry. Where are you with this? Edit. Sorry I misread the original post forget the above. I was talking about something irrelevent.

If it can be applied to the football pools, dogs or gee gees you will have many gullible takers.

Pete, what do you understand the periodic table to mean? What do you mean by a periodic structure when calculating Brillouin Zones? By periodic I mean that if f(a) is a solution then f(2a) is a solutions as is f(na). Or that something repeats regularly along at least one cordinate axis. Solitary travelling waves can be considered to repeat everywhere along an axis Solitary stationary waves are the combination of a wave within the stationary envelope and an envelope function.

Hello severin and thank you for taking an interest. But you are not really answering the question. The electric charge on quarks is +2/3 or -1/3 and on leptons is -1. This implies (to me at any rate) there is 'something' with a charge of 1/3 or -1/3 that I should be able to isolate and perhaps isolate three of them from a lepton.

pmb, in your original classical wave equation a is equivalent to my omega a period. The arbitrary functions F and G do not need of themselves to be periodic. In your later exposition of Schrodinger, n is periodic. As soon as you introduce some integer that can be 1..2..3..4.... you have introduced periodicity. And yes standing waves treat it differently from travelling waves. There would be no point in having the distinction otherwise. Of course a wave packet is localised. That is what the Fourier transform is about.

The only one that counts : My quotes came from the Oxford English Dictionary.

Neither I nor several famous English literary figures can agree with your teacher. Byron : I abhor death, because that thou must die Robert Burton : Annointing the doors and hinges with oil, because they should not creak. Of course there are cases for not inserting a comma and cases for using a full stop or other punctuation mark. 'Because' can be either an adverb or a conjunction. I think there is some choice about the issue depending upon the gap the author wishes to place into the text. As such both can be used with your steaming example. Kipling : I buy then because they are pretty. However he could have written I buy them, because they are pretty he added thoughtfully.

So how do you account for the fact that some elementary particles have charge and some don't? In other words why is there not an elementary charge carrier?

Forgive me, pmb but I thought the wave equation under discussion here was the schrodinger wave equation [math]i\hbar \left( {\frac{{\partial \psi }}{{\partial t}}} \right) = - \frac{{{\hbar ^2}}}{{2m}}\left( {\frac{{{\partial ^2}\psi }}{{\partial {z^2}}}} \right) + V\psi [/math] Which has solution the De Broglie waves given by [math]\psi = D{e^{i\left( {kz - \omega t} \right)}}[/math] Which is periodic in omega. You construct wave packets mathematically from two waves connected by fourier methods (series or transform) As for particle in the box and potential wells etc the mathematical solution function does indeed exist beyond the walls, but we just say it has no physical significance, since it coincides with what we want inside the box. Some figures. An electron accelerated through 1 volt has a De Broglie wavelength of 1.2 nm. This is ridiculously smaller than the dimensions of the smallest object in a CRT (the mask holes) so the passage is particle like. There is no such limiting obstruction in lecher lines so the wavelike behaviour can become apparent. Juanrga was challenged to calculate these several times, not just by myself and failed to do so. I also think at least some tunneling can be shown to be a characteristic of waves, not available to particulate behaviour.

Which question was that?

I agree. The one fundamental property of a wave is not probability it is periodicity. That is what I would expect to see brought out in any definition employing the use of the word wave. To go further than that it will require some thought.

No, I'm not happy with that definition. I think it is incomplete. Further it implies that the only fundamental entities are particles and that the probability function is somehow 'tacked on' and further that probabilities can only be applied to particles. I am old fashioned and think that it is far better in discussions for the promoter to start off by defining one's terms and the abbreviation symbols used in equations along with any restrictions of application. I always try to address a promoter's terms (not my own) unless I think a genuine mistake has been made.

The original atomic theory introduced the idea that the 'stuff of the universe' is made up from different arrangements of a small number of 'indivisible particles' . Each different such aprticle was identified with a particular element, from whence we obtain the modern term 'elementary particles' , which we still regard as indivisible. The original particles were subsequently found to be actually divisible into a smaller number of sub atomic particles which carried or mediated their observable properties and could be arranged diferently to form the original atoms of the theory. More recently (some of) these sub atomic particles have again been divided into particles which carry observable properties. this time a greater number of particles emerged. We now call these 'elementary particles'. However we have not atributed certain properties on a one to one basis to these elementary particles so some are properties are possessed by several. For instance charge is possessed by electrons and some quarks. So why do we believe that these are indivisible. Why are we not searching for an elementary indivisible particle that carries only charge?

I start from the premise that well intentioned posters want to see a correct post by themselves or anyone else - I certainly do. So sometimes I have been known to use the pm system "Hey Jack please check your figure in line 5 or whatever" If Jack then reworks his arithmetic (it's often a simple slip I like make all the time) no one else is any the wiser. I don't want the kudos of having publically pointed it out . So the first post (Jack's) ends up corrrect and there is no second post saying "Jack you are wrong and inviting argument." Fo me this is a win- win-win situations all round.