Measurement in quantum mechanics

The framework of quantum mechanics requires a careful definition of measurement. The issue of measurement lies at the heart of the problem of the interpretation of quantum mechanics, for which there is currently no consensus.

Measurement plays an important role in quantum mechanics, and it is viewed in different ways among various interpretations of quantum mechanics. In spite of considerable philosophical differences, different views of measurement almost universally agree on the practical question of what results form a routine quantum-physics laboratory measurement. To understand this, the Copenhagen interpretation, which has been commonly used, is employed in this article.

In classical mechanics, a simple system consisting of only one single particle is fully described by the position ${\displaystyle {\vec {x}}(t)}$ and momentum ${\displaystyle {\vec {p}}(t)}$ of the particle. As an analogue, in quantum mechanics a system is described by its quantum state, which contains the probabilities of possible positions and momenta. In mathematical language, all possible pure states of a system form an abstract vector space called Hilbert space, which is typically infinite-dimensional. A pure state is represented by a state vector in the Hilbert space.

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