Postulate of only time dependence on |ψ⟩

[LightPhoton]

Answers to questions like this assume that the quantum state in a Hilbert space is only a function of time, that is $\partial_i\vert\psi(t)\rangle\neq0$ only when the variable $i$ is $t$.

Is this a postulate of standard quantum mechanics, that in Schrödinger's equation the state in abstract only depends on time?

 

[PeroK]

Is this a postulate of standard quantum mechanics, that in Schrödinger's equation the state in abstract only depends on time?

What else could it depend on? What else could anything depend on?

 

[PeroK]

What else could it depend on? What else could anything depend on?

To explain what I mean by this. Let's take some function $E$, say, that describes the global socio-political-economic state. That state will change over time: $E(t)$. What else could it be a function of? Everything else is bundled into that function - population, political and economic policies etc.

The state tells you everything about a system at a point in time. The only free variable, if I can use that term, is time. You may be able to analyse the state at a point in time in many ways. But, if the state itself is complete, then time evolution is the only remaining variable.