An important feature of the wave equation is that its solutions
q(r, t) are uniquely specified once the initial values q(r, 0)
and (del)q(r, 0)/@t are specified. As was mentioned before, if
we view the wave equation as describing a continuum limit of a
network of coupled oscillators, then this result is very
reasonable since one must specify the initial position and
velocity of an oscillator to uniquely determine its motion. It
is possible to write down other “equations of motion” that
exhibit wave phenomena but which only require the initial values
of the dynamical variable — not its time derivative — to specify
a solution. This is physically appropriate in a number of
situations, the most significant of which is in quantum
mechanics where the wave equation is called the Schrodinger
equation. This equation describes the time development of the
observable attributes of a particle via the wave function (or
probability amplitude) . In quantum mechanics, the complete
specification of the initial conditions of th