- #1
mpkannan
- 15
- 0
It follows from the Expectation value postulate that an observable A, associated with the operator A^, can be precisely measured only if the wave function ψ of the system is an eigenfunction of A^ .
Accordingly, the position and momentum of a particle can never be precisely measured because the wave function (energy eigenfunction) is not an eigenfunction of the operators of these properties.
In the popular statement of the uncertainty principle, viz., the position and momentum of a particle cannot be measured precisely and simultaneously, it appears that one of these properties can be precisely measured sacrificing the other. Does it not contradict the above deduction from the expectation value postulate, that the wave function should be an eigenfunction of the operator of the property in order to measure the property precisely?
Accordingly, the position and momentum of a particle can never be precisely measured because the wave function (energy eigenfunction) is not an eigenfunction of the operators of these properties.
In the popular statement of the uncertainty principle, viz., the position and momentum of a particle cannot be measured precisely and simultaneously, it appears that one of these properties can be precisely measured sacrificing the other. Does it not contradict the above deduction from the expectation value postulate, that the wave function should be an eigenfunction of the operator of the property in order to measure the property precisely?