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A particle is in its ground state in a unidimensional potential well with infinitely high walls. Find the force with which the particle acts on the walls. Do the calculations for an electron in a well 10^(-10) m wide.

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Solution :For a particle in the ground state one de Broglie half-wave fits into the length of the potential well: `L=lamda//2`. The momentum of the particle is `p=h//lamda=h//2L`. The recoil of the particle from the wall of the well is perfectly elastic, so the change in its momentum is `Deltap=2p=h//L`. The average force of pressure is EQUAL to the product of the change in the momentum variation and the number of COLLISIONS PER unit time:
`F_(av)=Deltap*z=2p(V)/(2L)=p^(2)/(mL)=(h^(2))/(4mL^(3))`


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