how any one particle can be at 2 places at the same time as superposition theorem say ? how do we measure that superposition theorem is really acceptable ?
You can find some information at following link.
http://www.physics.org/article-questions.asp?id=124
we can not directly verify the superposition principle that means you can not see a particle floating around you at two(or many) different places at the same time .But we can say that if it was in two (or many) different places then the result will be like this.superposition principle can only be tested on the basis of the outcome of a particular experiment.For example double slit experiment for a single photon which shows interference pattern on the screen and only be explained if we assume that the photon was present in both the slit at the same time.
The superposition principle is a consequence of the fact that the Schrödinger equation is linear-so the sum of two solutions is a solution. It doesn't imply that a particle can be in more than one position at once-a statement that's meaningless.
The only role of the wavefunction is to produce the probability density, from which the calculation of the properties of position, momentum etc. can be realized.
I prefer this explanation: We do not know where exactly the photon was located during the described experiment! And we describe this ignorance with complex functions that satisfy the linear Schrodinger equation. A similar situation exists for classical particles when we do not know their initial conditions exactly, but then correlation functions appear that satisfy the corresponding linear equations :-)
Stam and all,
Browse this approach. It is a generalisation of a particle and consistent with planetary motions, if you assume they move on nco ( not necessarily all time, but parts of the ellipsoidal).
A circular path on a non-flat surface may be approximated as such.
Technical Report Tove time invariant Tti, exemplified with images from latera...
Planetary motion is classical, so it doesn't have anything to do with the subject.
The probabilistic properties of quantum mechanics aren't limited to a non-trivial probability density of the initial conditions-but express how to take into account configurations that don't solve the classical equations of motion, by providing a way for defining a probability measure for them.
It is well-known that Schrodinger Equation for a given problem admits more than one solution. Consider the quantum harmonic oscillator. It admits an infinite number of solutions each one having a particular energy eigenvalue. That means the general solution is a linear combination of all the solutions weighted by infinite number of complex coefficients, each one multiplying a given solution. This is linear superposition at the level of the wave function. Then you may ask that what is the probability that the given particle is in a given energy state? For example at the ground state? Or the first excited state?
It will be given by mod squaring complex coefficient; the one which is multiplying the state you are probing and which is already contained in the general solution. A particle cannot exist in two different energy states at a given time. Then you look at the shape of the wave function for a particular state: mod squaring wave function again, you get probability distribution function for a given energy state. As an example electrons in an atom moves in orbits of specific energy values. Transition from one energy state to another gives rise to emission and absorption type atomic spectra.
Now you may analyze probability distribution function to know about what is the probability that, in a given energy state, your particle will be found at a particular point in space. Obviously, while mod squaring wave function of a particular energy state time dependence will disappear which means that these states are stationary.
All this being said, I should add that I have talked only about non-relativistic, single particle quantum mechanics.
Remember that the state of a particle depends at least on two conjugate variables, for example position and momentum. The superposition principle doesn't simply mean that the particle can at two places at the same time, that is, that its state is the superposition of different localised states. Nor that we don't know where the particle is located, since instead of the position, the momentum could be measured, and there is no joint probability of position and momentum. The energy eigenstates don't play a privileged role, all the basis of the set of solution are equivalent. The superposition is better seen in interference experiments. When two different states superpose, they generally interfere given fringes. In the two slit experiment, each slit selects a particular state so that the interference pattern be visible.
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