(6-1)  The separation of the space and time-dependent variables means that we can straightforwardly differentiate Ψ(x,t) with respect to time, as the ψ(x) term is not a function of time, and therefore behaves just like a constant in this operation:

①  Differentiate twice to find ∂2Ψ(x,t)/ ∂t2

 

②  Notice that you can express your answer in terms of Ψ. Do this.

 

③  Now apply the wave equation (equation VI-3) to find an expression for ∂2 Ψ (x,t)/ ∂x2

 

④  Deduce the expression for d2ψ(x)/dx2.