As an application of the Schrodinger equation, we now calculate the states of a particle in an oscillator potential. From classical mechanics we know that such a potential is of greater importance, because many complicated potentials can be approximated in the vicinity of their equilibrium points by a harmonic oscillator. Expanding a potential V(x) in one dimension in a Taylor series yields $$ \begin{gathered} V\left( x \right) = V\left( {a + \left( {x - a} \right)} \right) \hfill \\ = V\left( a \right) + V'\left( a \right)\left( {x - a} \right) + \frac{1} {2}V''\left( a \right)\left( {x - a} \right)^2 + \ldots . \hfill \\ \end{gathered} $$ (7.1)