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Schrodinger equation for a free particle is

i[itex]\hbar[/itex]∂ψ(x,t)/∂t = (-[itex]\hbar[/itex]

^{2}/2m)(∂

^{2}ψ(x,t)/∂x

^{2})

Here (∂

^{2}ψ(x,t)/∂x

^{2}) is second power of ψ. Then how can we justify the statement "second or higher powers of ψ do not appear"?