Definition of "state" in QM

1. Jul 10, 2015

lightarrow

Mathematically, a state in QM is a ray on the Hilbert space. But:
1) How would you define "state" from a physical point of view? I know a lot of examples but not a general definition.
2) Given a specific quantum system, to find all the states and so the Hilbert space, all I have to do is to solve the SchrÃ¶dinger equation (when this is possible)?

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lightarrow

2. Jul 10, 2015

atyy

We don't know whether a state is real in quantum mechanics. However, even if we take an operational view of the state, we can pretend that it is real. So reality is just a tool to calculate the probabilities of measurement outcomes.

However, given a choice of observables, commutation relations and Hilbert space, a traditional Copenhagen interpretation is it that a pure quantum state is the complete description of a single quantum system. Although this is sometimes contrasted with an ensemble view, the traditional view is also an ensemble view, because it assumes that the state only permits probabilistic predictions via the Born rule. This is why the traditional view is also called the Statistical Interpretation.

Last edited: Jul 10, 2015
3. Jul 10, 2015

stevendaryl

Staff Emeritus
An operational definition of "state" in QM is that the state is a function which, given any observable, returns the expectation value for that observable. So it's just a way of computing statistical predictions for outcomes of future observations. That doesn't give much insight into what's going on, physically, but there isn't a good consensus about that, anyway.

4. Jul 10, 2015

lightarrow

With this definition, the function defining the state isn't unique, is it?

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lightarrow

5. Jul 10, 2015

lightarrow

So it's not always easy to identify which are all the possible informations about the system, especially after it has interacted with something? E.g., how can I know if the state has changed or not? if a light photon goes through a transparent crystal, does its state change?

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lightarrow

6. Jul 10, 2015

atyy

Generally, the quantum mechanical framework involves observables, states, Hamiltonians etc, which is an empty outline that must be filled in with specifics. If the physicist believes this outline is true, then his job is to figure out the specific forms to fill in these empty outlines in a way that is consistent across all his experiments.

It is not different from classical physics and F = ma, which is just a meaningless outline unless we give specific forms for F, eg: F = Gmm/r2 for gravitation.

Similarly, how the state of a photon is changed by going through a transparent crystal may be specified by putting a term in the Hamiltonian that specifically describes the interaction between the photon and the crystal (that's overkill sometimes, but it's more or less right).

7. Jul 10, 2015

lightarrow

Thanks to both of you.

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lightarrow.