Markov property: compatible with momentum?

  • I
  • Thread starter lolcopters
  • Start date
  • #1

Main Question or Discussion Point

Say I'm simulating the movements of two interacting atoms. Could this system have the markov property (the future positions of the atoms depend only on the current position, not the past)?
What's got me on the fence are the atoms' momentums: it's a property of the present state (at time t, the momentum is p), but its value depends on past states. So does anyone know if a system like this could have the markov property?
Thanks
 

Answers and Replies

  • #2
DrClaude
Mentor
7,163
3,308
You misunderstood what Markov is about. Of course, the state of any system at time t0 depends on what happened at times t < t0. But in a Markovian process, there is no memory of how the state at time t0 was reached. All that is important is that the state at time t0 completely describes the system (and its future evolution).

In the case of two atoms governed by a known Hamiltonian, given the wave function ψ(t0) of the two-atom system, one can calculate ψ(t) for any t > t0. No need to know the wave function for any time < t0.
 
Last edited:
  • #3
Stephen Tashi
Science Advisor
7,023
1,244
Say I'm simulating the movements of two interacting atoms. Could this system have the markov property (the future positions of the atoms depend only on the current position, not the past)?
It isn't meaningful to ask whether a physical system has the markov property until you say what variables you will choose to define a "state". A physical system may have the markov property when one definition of "state" is used and not have it when a different definition is used.

Are you considering actual atoms - or just thinking about "point particles" ?

You only mention "position" as the variables involved in your definition "state" ? Did you intend to omit variables like mass, velocity and acceleration ?
 

Related Threads on Markov property: compatible with momentum?

Replies
8
Views
2K
  • Last Post
Replies
15
Views
1K
  • Last Post
Replies
10
Views
2K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
23
Views
1K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
3
Views
4K
  • Last Post
Replies
8
Views
2K
Top