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## Main Question or Discussion Point

Dear all,

Intuitively, the probability of finding a trapped particle at a given location x should be proportional to the inverse of the velocity of the particle. But for even the simplest of systems, such as 1D harmonic potential SHM, the velocity is zero at the two end points (+A & -A) of the motion. This makes 1/v(x) not defined for x=+A & -A. How is this intuitively possible according to classical mechanics only?

On a side note, I am actually trying to find rdot as a function of r or t for a central force problem with potential proportional to r^3. Anyone tackled such a problem? :)

Cheers.

Intuitively, the probability of finding a trapped particle at a given location x should be proportional to the inverse of the velocity of the particle. But for even the simplest of systems, such as 1D harmonic potential SHM, the velocity is zero at the two end points (+A & -A) of the motion. This makes 1/v(x) not defined for x=+A & -A. How is this intuitively possible according to classical mechanics only?

On a side note, I am actually trying to find rdot as a function of r or t for a central force problem with potential proportional to r^3. Anyone tackled such a problem? :)

Cheers.