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position operator : ウィキペディア英語版
position operator
In quantum mechanics, the position operator is the operator that corresponds to the position observable of a particle. The eigenvalue of the operator is the position vector of the particle.
==Introduction==

In one dimension, the square modulus of the wave function, |\psi|^2 = \psi^
* \psi , represents the probability density of finding the particle at position x . Hence the expected value of a measurement of the position of the particle is
: \langle x \rangle = \int_^ x |\psi|^2 dx = \int_^ \psi^
* x \psi dx
Accordingly, the quantum mechanical operator corresponding to position is \hat , where
: \hat \psi(x) = x\psi(x)
The circumflex over the x on the left side indicates an operator, so that this equation may be read ''The result of the operator x acting on any function ψ(x) equals x multiplied by ψ(x).'' Or more simply, ''the operator x multiplies any function ψ(x) by x.''

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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