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DaveC426913

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The wavefunction isn't physical - remember it's describe by complex quantities. What is a physically representable property is the wavefunction (in position representation) squared, which gives the probability of finding the particle in a certain point in space (or describes your 'cloud' if you like). What is also 'physical' is information you can get from the system at a given time (I forget the orginator, but the quote 'Information in Physical' applies here!).

These other 'physical' quantities result from measurements on the wavefunction. For example, the momentum operator is [itex]\hat p = -i\hbar\nabla[/itex], and the position operator is [itex]\hat x = x[/itex]. You perform a measurement of the operator on a wavefunction and the wavefunction then collapses to the eigenvector corresponding to the eigenvalue you measured. Note in the momentum and position case, these eigenvectors / values form a continuous spectrum, as oppoed to, say, a measurement of spin.

So, how much 'physical' information can we get out of a system? This is where the HUP plays a role (well, really where it's derived from). There is a function on operators (well, actually it's another operator) called the commutator, defined as [A,B] = AB - BA. If this doesn't equal 0, then the two operators can't be measured together to arbitary precision. From working out expectation values of measurements on [itex]\hat p[/itex] and [itex]\hat x[/itex] the HUP can be derived.

Note as an interesting 'side effect' / property of operators that do commute (and therefore can be measured together) - they share the same eigenspace.

So, the wavefunction is abstract, but we can get physical information by measuring operators on it.

These other 'physical' quantities result from measurements on the wavefunction. For example, the momentum operator is [itex]\hat p = -i\hbar\nabla[/itex], and the position operator is [itex]\hat x = x[/itex]. You perform a measurement of the operator on a wavefunction and the wavefunction then collapses to the eigenvector corresponding to the eigenvalue you measured. Note in the momentum and position case, these eigenvectors / values form a continuous spectrum, as oppoed to, say, a measurement of spin.

So, how much 'physical' information can we get out of a system? This is where the HUP plays a role (well, really where it's derived from). There is a function on operators (well, actually it's another operator) called the commutator, defined as [A,B] = AB - BA. If this doesn't equal 0, then the two operators can't be measured together to arbitary precision. From working out expectation values of measurements on [itex]\hat p[/itex] and [itex]\hat x[/itex] the HUP can be derived.

Note as an interesting 'side effect' / property of operators that do commute (and therefore can be measured together) - they share the same eigenspace.

So, the wavefunction is abstract, but we can get physical information by measuring operators on it.

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