The formula T = -(ħ/2m)∇(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}implies that T is proportional to the second spatial derivative of a wavefunction. What is the origin of this dependence?

In classical mechanics, T = p^{2}/2m. Is it also the case in classical mechanics that p^{2}/2m is proportional to a second spatial derivative? I have not been able to relate (d/dt)^{2}to d^{2}/dx^{2}using classical mechanics.

Thanks,

Steven

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# I Why does the kinetic operator depend on a second derivative?

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