(The following is a purely qualitative consideration of Quantum Mechanics)(adsbygoogle = window.adsbygoogle || []).push({});

In a particular Quantum Mechanics text, I've come across the following quote which I'm having some difficulties interpreting.

"We describe the instantaeous state of the system by a quantity [itex] \Psi [/itex], which satisfies a differential equation, and therefore changes with time in a way which is completely determined by its form at a time t = 0, so that its behavior is rigorously causal. Since, however, physical significance is confined to the quantity [itex] \Psi^{*} \Psi [/itex], and to other similarly constructed quadratic expressions, which only partially define [itex] \Psi [/itex], it follows that, even when the physically determinable quantities are completely known at a time t = 0, the initial value of the [itex] \Psi [/itex] function is necessarily not completely definable. This view of the matter is equivalent to the assertion that events happen indeed in a strictly causal way, but that we do not know the initial state exactly."

-- Max Born

I understand that [itex] \Psi [/itex] contains some information that cannot be obtained from [itex] \Psi^{*} \Psi [/itex] (for instance, the imaginary part, or its sign), but this doesn't mean that [itex] \Psi [/itex] is notdeducablefrom the Hamiltonian through the Schordinger equation.

Is the point that Born is trying to make that, although we can deduce the quantity [itex] \Psi [/itex] mathematically with some prior physical knowledge (namely, the Hamiltonian), we can never directly measure [itex] \Psi [/itex] itself? What does he mean by "not completely definable"? This seems a very important point.

Thanks.

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# Born's Interpretation of Wavefunctions

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