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Heisenberg's uncertainty principle

Any pair of complementary observables cannot be determined simultaneously. In other words we cannot specify the eigenvalues of any two non-commuting operators. We have already seen in the previous subsection that the position along x axis and x component of the linear momentum are complementary variables. Hence they cannot be determined simultaneously.

Werner Heisenberg in 1927 proposed the following relation, now known as the famous Heisenberg's uncertainty principle:

*x* and
*p*_{x} are the respective uncertainties in the simultaneous determination of *x* and *p*_{x}. Even if it be possible to measure *x* with certainty, according to the principle the determination of *p*_{x} would become totally uncertain.

In this context, it may be mentioned that the very act of measurement introduces uncertainties in the values of the complementary observables leading to a change of state of the system.

Heisenberg went on to receive the Nobel prize in Physics in the year 1932 for his contribution to the birth of quantum mechanics.

*Abhijit Poddar *

2007-09-27