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## Main Question or Discussion Point

As part of proving that d/dt <p> = <-Del V> you have to use the fact that < dp/dt> = 0 when p is not an explicit function of time.

I'm not clear on what this means. Any insights to share?

From classical mechanics, if there is a potential V = -k/r then there will be a force on a particle and the momentum will evolve over time. In Q-M, this is an implicit function of time and so still <dp/dt > = 0.

An explicit function of time would be V = -kcos(t) / r and now

< dp/dt> is not equal to zero. p still evolves over time.

I can't see why implicit or explicit function makes any difference mathematically.

I'm not clear on what this means. Any insights to share?

From classical mechanics, if there is a potential V = -k/r then there will be a force on a particle and the momentum will evolve over time. In Q-M, this is an implicit function of time and so still <dp/dt > = 0.

An explicit function of time would be V = -kcos(t) / r and now

< dp/dt> is not equal to zero. p still evolves over time.

I can't see why implicit or explicit function makes any difference mathematically.