psi.p(x) = A cos(2pix/lambda) = Acos( px/h) | (1) |
psi.p(x) = Ae^(ipx/h) | (2) |
d^2y/dt^2 = c^2 d^2d/dx^2 | (3) |
The simplest example is the calculation of the speed of a particle. In the first measurement you are supposed to measure both the position and the time of the particle. The problem is this measurement will always influence the position and direction of the particle. The result is, that at the moment when the particle is measured for the second time, the position of particle will be different compared with the supposed position, as if the first measurement did not took place. That means the calculated speed is wrong.
To say this in a different way: The value of the calculated speed is uncertain, caused by the measurement process. But, and that is important, that does not mean that the positions and velocity at any moment are uncertain. It is the other way around: At any moment in time, both the position and the speed of any particle have a certain value. Except we humans are not capable to measure or calculate these parameters, acurate.
Even more problematic is the calculation of momentum of a particle. The momentum is the product of the speed of the particle times the mass of a particle. To calculate the speed is discussed previous. To calculate the mass of a particle or an object requires Newton Law. That means you have to trace the trajectory over 'a long period of time', which involves many measurements.
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