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In axiomatic formulation of quantum mechanics, quantum states are postulated as vectors residing in Hilbert space.

The only apriori requirement that Iam aware of ,for a quantity to qualify as a quantum state, is that it should obey principle of superposition ,which a scalar quantity would obey as good as a vector.

Then why don't we take quantum states as scalars?

What I think could be the reason:

Quantum states are characterized by certain dynamical variables

In standard formalism we represent dynamical variables as operators acting as linear transformation on vectors.

Now,scalars are not operated on by operators,so by taking scalars as quantum states we can no longer characterize a quantum state by physically observable properties,which would render it meaningless.

I would really like to know whether my answer is correct.

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# Quantum states as scalars

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