Both the classical and quantum mechanical probability densities predict for a simple harmonic oscillator that

a. the probability of the particle being at that location will be greatest at regions of greatest potential energy.
b. the particle has a finite probability of being in a region with V > E, where E is the total energy of the system.
c. at very large values of n (the number of energy state), the particle will most likely be detected furthest from the equilibrium position within its classically defined range of motion
d. the minimum energy of the oscillating particle is zero

c.
At energies near the classical realm, both models predict the particle oscillating to be detected most often—that is, the highest probability of being at that point—furthest away from the equilibrium point. The two must match up because of Bohr's correspondence principle.

Physics & Space Science

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