Heisenberg''s uncertainty principle of position & momentum, Physics

Q. Heisenberg's uncertainty principle of position & momentum. Describe an experiment to study the uncertainty of position & momentum. 

Heisenberg's Uncertainty Principle : It is impossible to know simultaneously and with exactness both the position and the momentum of the fundamental particles constituting matter. The optimum precision is the knowledge of position and momentum is determined by following equation

If the location of a particle is very precise our knowledge of the momentum of the particle is nil and we have no idea about the momentum of the particle.

Hence it is impossible to know both the exact momentum error in a given direction of a particle at the same time. Heisenberg uncertainty principle can also be stated as it is not possible to make a simultaneous determination of the energy and the time coordinate of a particle with unlimited precision.

Suppose a narrow beam of electron is incident on a slit AB of width and produces a diffraction pattern on the screen. If the first minimum is obtained in the diffraction pattern in a direction from the direction of incidence, then from the diffraction formula

When electrons are incident on the slit, we can't say definitely that which electrons will fall at what place of the slit, i.e. the uncertainty I determining the position of the electrons will be equal to the width of the slit.

Initially the electrons is moving along the x direction, so the momentum in the y direction will be zero. After diffraction at the slit the electron may be diffracted at any angle from. Therefore the y component of momentum of electron can be any value between P sin and -P sin.

 

 

Posted Date: 7/11/2012 3:12:06 AM | Location : United States







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