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show the expectation value of the kinetic energy in a bound state described by the spherically symmetric wavefunction [itex]\psi_T(r)[/itex] may be written

[itex] \langle \hat{T} \rangle = \frac{\hbar^2}{2m} \int \int \int \vline \frac{\partial \psi_T}{\partial r} \vline^2 d^3r[/itex]

so far i have

[itex] \langle \hat{T} \rangle = -\frac{\hbar^2}{2m} \int_V \psi^* \nabla^2 \psi d^3r[/itex]

usually one uses integration by parts here (at least in the 1D case) but that got me lost and so i tried expanding the laplacian in spherical polars but then the terms didn't cancel properly. any ideas?

thanks.