Engineering Physics: Unit IV: Basic Quantum Mechanics
Probability Density
Quantum Mechanics
Probability of finding the particle between positions x and x + dx
PROBABILITY DENSITY Probability of finding the particle between positions x and x + dx Probability density is maximum when • For n = 1 (lowest energy state), x = a/2, i.e., the particle is most likely to be in the middle of the box (because • For n = 2 (next energy state), • For n = 3, the most likely positions of particle are The variation of probability densities It is noted that quantum mechanical results vary drastically from the classical results. While classical mechanics predicts the same probability for the particle being anywhere in the box, quantum mechanics predicts that the probability is different at different points and there are points (nodes) where the particle is never found.
is maximum there).
the particle is most likely to be at 
and never found in the middle because 
is zero there.
(for n = 1, 2, 3) with x is shown in fig. 6.13.
Engineering Physics: Unit IV: Basic Quantum Mechanics : Tag: : Quantum Mechanics - Probability Density
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Engineering Physics
PH3151 1st semester | 2021 Regulation | 1st Semester Common to all Dept 2021 Regulation