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The evolution of a wavefunction describing a physical system under this equation is normally taken to be perfectly deterministic.[7] If one adopts an interpretation of QM according to which that's it i.e., nothing ever interrupts Schrödinger evolution, and the wavefunctions governed by the equation tell the complete physical story then quantum mechanics is a perfectly deterministic theory.
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The linearity assumption then implies that this holds for arbitrary input signals f. Since H ˆ commutes with both A ˆ and B ˆ, the basic equation tells us that a ∂ ∂ a H W f ( a, t ) = κ H W f ( a, t ) − α W f ( a, t ) − a β ∂ ∂ t H W f ( a, t ) + a κ ∂ ∂ t W f ( a, t ).
Now, it follows from (3.1), above, that there are states of S (too many to count) which are not eigenstates of A, and if we consider what Schrödinger's equation tells us about the joint evolution of S and S* when S is started out in one of these, we find that the state of the pair after interaction is a superposition of eigenstates of [A on S & B on S*].
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com