Ever since 10th grade when i got to know that electron is *also* a wave i have been wondering if electron is a wave then "whats waving?" When i asked my physics teacher this he threw me out of class (almost :) ) I understand in case of photon i guess the electromagnetic field is waving but whats waving in case of other stuff (electron and other brothers)
If by waving you mean the Wavefunction of the electron, then the interpetration for the wavefunction of the electron is probability density. To be more accurate, if [tex]\psi(x,t)[/tex] is the qunatum amplitude (a function obtained by Schrodinger's Equation) of the electron, at any given point x (might be one-dimensional or three-dimensional) at any time t, then the function [tex]P(x,t)=|\psi(x,t)|^{2}[/tex] is the probability density of finding the electron in a point x at time t. (Notice that [tex]\psi[/tex] is a complex number, while the probability density is a real number) So in quantum mechanics, waving is interepted as "being situated at an indefinite position" - as long as you don't directly measure its position, from your point of view the electron exists simultanousley at a certain region of space rather than in a specific point.
According to my understanding waves are produced when something is waving... like a bunch of people *oscilating* to produce a mexican wave at the football stadium or the water waves where the water moves up and down to create a wave, in that sense what is waving when we say an electron is waving. i understand that the mathematical formalism suggest that the probability density is waving (going up and down) but what is the physical manifestation of probabilty density how do you define it physically
There are a number of elements of quantum theory for which the physical representation is unknown. This is one of them. The Pauli exclusion principle and the Heisenberg Uncertainty Principle, as well as virtual particles, are parts of the quantum formalism which have no clear classical analog. That should not be considered a true weakness of the theory however. Of course it would be desirable to have a picture or model. That is why the so-called interpretations of quantum mechanics were developed. There is no one satisfactory interpretation at this point, it is just your personal preference. So the answer to what is waving is: whatever you want it to be. Or nothing. The key is that the mathematical formalism is taken seriously, and that you consider your model as a convenient approximation used for discussion purposes. But don't confuse your model with reality as that becomes problematic eventually.
Quantum particles, such as electrons and photons, are not waves. But, if we perform an experiment to determine the position of the particle, we obtain its "wavefunction" by solving Schrodinger's equation in the position representation. This wavefunction squared is a probability density, from which we can determine the probability distribution of all possible positions that can result when position is measured. (This is the Born interpretation, the only interpretation that has near universal acceptance.) It is this probability density that often has maxima and minima familiar to us from wave interference. But, there is nothing "waving" here! Although we have a wavefunction, it does not describe a continuum that vibrates when the wavefunction is present. These are probability waves, not mechanical waves or electromagnetic waves. They are not real and are not observable. Also, this wavefunction is not the particle. Nor does it describe the behavior of the particle.Yet, it is not uncommon to confuse the particle with the wavefunction; it is incorrect to say, "the electron is a wave". Further, an electron, or any quantum particle, never "exists simultanousley at a certain region of space rather than in a specific point." A quantum particle is, indeed, always detected at a specific point.