The infinite square well potential is given by:
This is illustrated below.
A particle under the influence of such a potential is free - no forces act - between
and
and is confined to that region by the need to have an infinite energy in order to travel outside that region. We can solve the equations describing the motion of the particle in each region and make them fit together at the boundaries using the conditions, for wavefunctions
and 
on either side of the barriers that
and
In the region of the well,
and the Schrodinger equation becomes
(1)
This has general solution
atand
since the potential is infinite there, so
so
and
We can find the constant
by requiring that the wavefunction
be normalized so
We can differentiatetwice to get
so from (1)