Basic concepts of quantum mechanics: Difference between revisions

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[[File:Heisenberg 10.jpg|thumb|left|125px|Werner Heisenberg at the age of 26. Heisenberg won the [[Nobel Prize in Physics]] in 1932 for the work that he did at around this time.<ref>[http://nobelprize.org/nobel_prizes/physics/laureates/1932/ Heisenberg's Nobel Prize citation]</ref>]]Suppose that we want to measure the position and speed of an object -- for example a car going through a radar speed trap. Naively, we assume that (at a particular moment in time) the car has a definite position and speed, and how accurately we can measure these values depends on the quality of our measuring equipment -- if we improve the precision of our measuring equipment, we will get a result that is closer to the true value. In particular, we would assume that how precisely we measure the speed of the car does not affect its position, and vice versa.

In 1927 German physicist [[Werner Heisenberg]] proved that in the subatomicsub-atomic world such assumptions are not correct.<ref>Heisenberg first published his work on the uncertainty principle in the leading German physics journal ''Zeitschrift für Physik'': {{Cite journal|first1=W.|last=Heisenberg|title=Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik|journal=Z. Phys.|volume=43|year=1927|pages=172–198|doi=10.1007/BF01397280}}</ref> Quantum mechanics shows that certain pairs of physical properties, such as position and speed, cannot both be known to arbitrary precision. He showed that the more precisely one of them is known, the less precisely the other can be known. This statement is known as the [[uncertainty principle]] (or Heisenberg's uncertainty principle). It is not a statement about the accuracy of our measuring equipment, but about the nature of the system itself -- our naive assumption that an object has a definite position and speed is incorrect. On a scale of cars and people, these uncertainties are still present but are too small to be noticed; yet they are large enough that when dealing with individual atoms and electrons they become critical.<ref>[http://nobelprize.org/nobel_prizes/physics/laureates/1932/press.html Nobel Prize in Physics presentation speech, 1932]</ref>

Heisenberg gave, as an illustration, the measurement of the position and momentum of an electron using a photon of light. In measuring the electron's position, the higher the frequency of the photon the more accurate is the measurement of the position of the impact, but the greater is the disturbance of the electron, which absorbs a random amount of energy, rendering the measurement obtained of its [[momentum]] increasingly uncertain (momentum is velocity multiplied by mass), for one is necessarily measuring its post-impact disturbed momentum, from the collision products, not its original momentum. With a photon of lower frequency the disturbance - hence uncertainty - in the momentum is less, but so is the accuracy of the measurement of the position of the impact.

The uncertainty principle shows mathematically that the product of the uncertainty in the position and [[momentum]] of a particle can never be less than a certain value, and that this value is related to Planck's constant. (actuallyIt approximatingis, veryin closelypoint of fact, up to a valuesmall ofnumerical one-halffactor ofequal to Planck's constant).

==Schrödinger's wave equation==