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when a body is subjected to $0 K$ temperature, it becomes rigid. hence if we see in terms of quantum the lattice vibration decreases, resulting in no change in the direction of the Random velocity, then can we increase the degree of probability of finding of an electron in an given sys

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A body CANNOT be subjected to a 0 K temperature. – Schlomo Apr 29 '13 at 15:05

You say:

when a body is subjected to 0 k temperature , it becomes rigid

but this isn't true because vibrating systems (usually) posess zero point energy. A good example of this is that Helium remains a liquid even at absolute zero. I would guess you're wondering if the uncertainty principle can be violated at absolute zero, but in fact zero point energy exists because the uncertainty principle cannot be violated.

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