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• The momentum operator p/ for
the particle along x axis is
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n this case f(x) is called an eigenfunction of ˆA and a the corresponding eigenvalue. and since by the de Broglie relation ¯hk is the momentum p of the particle, we have pf(x) = pf(x) Note that this explains the choice of sign in the definition of the momentum operator!
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The momentum operator p/ for the particle along the x-axis is the fundamental operator.
- Neither the operator nor the wave function has any meaning.
- An operator is a mathematical commodity that enco des a "quantum version of observable" (while the observable itself is a parameter), and a wave function is an abstract "thing" that represents quantum states (often in the form of a complex vector).
- If we square that wave function or apply an operator to it, we will receive the parameter's average/expectation value.
- As a result, the relationship is essentially mathematical because the operator and wavefunction are mathematical objects.
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