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- Show that the average value of kinetic energy for a particle in one dimension having the wave function \(\psi(x)\) is \[ \langle \text{K.E.}\rangle = \frac{\hbar^2}{2m}\int_{-\infty} ^ \infty |\psi(x)|^2\, dx.\]
- Obtain a similar formula for the average of kinetic energy in three dimensions for a particle if the wave function \(\psi(r)\) is independent of polar coordinates \(\theta, \phi\).
- Can one write down a similar result for the general case in polar coordinates when the wave fucntion depends on all the three variables \(r,\theta,\phi\)?
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4727:Diamond Point
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