Ensemble interpretation

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Quantum mechanics
${\displaystyle i\hbar {\frac {d}{dt}}|\Psi \rangle ={\hat {H}}|\Psi \rangle }$ Schrödinger equation
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The ensemble interpretation of quantum mechanics considers the quantum state description to apply only to an ensemble of similarly prepared systems, rather than supposing that it exhaustively represents an individual physical system.^[1]

The advocates of the ensemble interpretation of quantum mechanics claim that it is minimalist, making the fewest physical assumptions about the meaning of the standard mathematical formalism. It proposes to take to the fullest extent the statistical interpretation of Max Born, for which he won the Nobel Prize in Physics in 1954.^[2] On the face of it, the ensemble interpretation might appear to contradict the doctrine proposed by Niels Bohr, that the wave function describes an individual system or particle, not an ensemble, though he accepted Born's statistical interpretation of quantum mechanics. It is not quite clear exactly what kind of ensemble Bohr intended to exclude, since he did not describe probability in terms of ensembles. The ensemble interpretation is sometimes, especially by its proponents, called "the statistical interpretation",^[1] but it seems perhaps different from Born's statistical interpretation.

As is the case for "the" Copenhagen interpretation, "the" ensemble interpretation might not be uniquely defined. In one view, the ensemble interpretation may be defined as that advocated by Leslie E. Ballentine, Professor at Simon Fraser University.^[3] His interpretation does not attempt to justify, or otherwise derive, or explain quantum mechanics from any deterministic process, or make any other statement about the real nature of quantum phenomena; it intends simply to interpret the wave function. It does not propose to lead to actual results that differ from orthodox interpretations. It makes the statistical operator primary in reading the wave function, deriving the notion of a pure state from that.