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Consider a dynamical system consisting of a single nonrelativistic particle of mass moving along the axis in some real potential . In quantum mechanics, the instantaneous state of the system is represented by a complex wavefunction . This wavefunction evolves in time
according to Schrödinger's equation:

(137) 
The wavefunction is interpreted as follows:
is
the probability density of a measurement of the particle's
displacement yielding the value . Thus, the probability of
a measurement of the displacement giving a result
between and (where ) is

(138) 
Note that this quantity is real and positive definite.
Richard Fitzpatrick
20100720