**Fig. 2-4. ** Probability distributions *P*_{n}(x)
for an electron confined to move on a line of fixed length in the quantum
levels with n = 1, 2, ..., 6. The area of each rectangle shown in thefigure
for *P*_{1}(x)
equals the probability that the electron is in the particular segment of
the line D*x *forming the base of the rectangle.
The percentage shown in each rectangle is the percentage
probability that the electron is in a particular segment D*x*.
The total probability that the electron is somewhere on the line is given
by the total area under the *P*_{1}(x)
curve, that is, by the sum of each small element of area *P*_{1}(x)D*x*
for each segment D*x*. This total area
is made to equal unity for every *P*_{n}(x)
curve by expressing the values of *P*_{n}(x)
in units of (1/L). Thus by definition a prbability of one denotes a certainty.