# Describing a system by position and momentum.

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1. Apr 30, 2015

### Ananthan9470

We often come across the statement, 'any measurable quantity of a system can be known by knowing its position and momentum'. I do not understand this. If position and momentum of a particle is given, how do we know its velocity? For that, mass also has to be specified right?

2. Apr 30, 2015

### jbriggs444

If you know position as a function of time then you know both velocity and acceleration. If you know velocity and momentum then you know mass.

That said, I have never encountered the statement you quote.

3. Apr 30, 2015

### BruceW

I think the idea is from (classical) Hamiltonian mechanics. If we have the Hamiltonian of the system (which is a function of generalised coordinates and momenta), then if we also know all the generalised coordinates and momenta at some given time, then we can say exactly how any quantity of the system will evolve from that time onwards. And note that we don't need to know about masses, since all that information is contained in the Hamiltonian. Or at least, all the information that is relevant to the time evolution of the system is contained in the Hamiltonian.

So really, instead of "any measurable quantity of a system can be known by knowing its position and momentum", it might be better to say that "the time evolution of any measurable quantity of a system can be known by knowing the Hamiltonian of the system, and all generalised coordinates and momenta at a given time".

edit: at least, I think this is most likely what the OP'er had come across. This is a bit of guesswork, the OP'er's quote could have come from some other principle.