Laws of nature must be built into the matrices

Heisenberg's next task was to determine what kind of matrices should represent different physical observables. At this point it becomes necessary to match theory with experiment, and to put experimentally determined numbers into the theory, which so far was completely abstract.

Heisenberg's best-known and most basic discovery involved the observables position and momentum. He found that the matrices representing the position and momentum of a particle such as an electron or a proton must obey the following commutation condition:

where

Law of Nature governing coordinate q and momentum p.

p] is a matrix representing the physical observable 'momentum', [q] is a matrix representing the physical observable 'position', [I ] is the unit matrix, and h is Planck's constant, and i = ^-1 .

More specifically, if we consider a particular coordinate, say in the x direction, ih

2p where px is the component of momentum in the x direction.

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