How are degrees of freedom understood in QM?

[Posy McPostface]

I'm having a hard time understanding 'degrees of freedom'. Could someone please provide an example in terms of Quantum Mechanics about what a 'degree of freedom' could be represented as? Is it simply a number of observations of a physical system to determine the arrangement of particles within that system? Does the accuracy increase with a number of observations made or is one observation enough?

On a deeper level, is there a demarcation that can be said about the observer and the state space of a system or does that line blur away once an observation is made?

 

[A. Neumaier]

For a system of N particles, the number of degrees of freedom is 3N, one for each position coordinate of each particle. On the other hand, a quantum field has an infinite number of degreeess of freedom.

This is the most typical usage. In a generalized sense, one may consider other (e.g., spin) coordinates as degrees of freedom but this is far less common (and must be inferred from the context).

In any case, this has nothing to do with observation.

The observer is conventionally always assumed to be completely outside the observed system, and hence not represented in the latter's state space.

 

[Posy McPostface]

The observer is conventionally always assumed to be completely outside the observed system, and hence not represented in the latter's state space.

Thank you for the explanation. I understand now.

Doesn't the observer interact with the system by observing it and thus affecting the degrees of freedom in the new observer-state space?

 

[A. Neumaier]

Thank you for the explanation. I understand now.

Doesn't the observer interact with the system by observing it and thus affecting the degrees of freedom in the new observer-state space?

Observation doesn't change the degrees of freedom but only the particular state in the state space of the system.