The Uncertainty Principle

The Heisenberg uncertainty principle, given in 1927, also applies primarily to very
small particles, and states that we cannot describe with absolute accuracy the hchavior
of these subatomic particles. The uncertainty principle describe a fundamental
relationship between conjugate variables, including position and momentum and also
energy and time.
The first statement of the uncertainty principle is that it is impossible to simultaneously
describe with absolute accuracy the position and momentum of a particle. If
the uncertainty in the momentum is delta p and the uncertainty in the postion is Ax, then
the uncertainty principle is stated as

The second statement of the uncertainty principle is that it is impossible to simultaneously
describe with absolute accuracy the energy of a particle and the instant
of time the particle has this energy. Again. if the uncertainty in the energy is given by
AE and the uncertainty in the time is given by Ar, then the uncertainty principle is
stated as


One way to visualize the uncertainty principle is to consider the simultaneous
measurement of position and momentum, and the simultaneous measurement of energy
and time. The uncertainty principle implies that these simultaneous measurements
are in error to a certain extent. However, the modified Planck's constant ti is very
small; the uncertainty principle is only significant for subatomic particles. We must
keep in mind nevertheless that the uncertainty principle is a fundamental statement and
does not deal only with measurements.
One consequence of the uncertainty principle is that we cannot. for example. determine
the exact position of an electron. We will, instead, determine the probability
of finding an electron at a particular position. In later chapters, we will develop a
probability density function that will allow us to determine the probability that an
electron has a particular energy. So in describing electron behavior, we will he dealing
with probability functions.

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