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This is an extract from the lecture notes I took for the 'Foundations of QM' third year course.

State: wavefunction ψ(x); (ψ,[itex]\varphi[/itex]) = [itex]\int d^{3}r ψ^{*}(r)\varphi(r)[/itex]

Evolution: TDSE

Observables ([itex]\hat{x},\hat{p},\hat{H}[/itex]): A = A-dagger; {x,p} = 1 [itex]\rightarrow[/itex] [itex][\hat{x},\hat{p}][/itex] = i[itex]\hbar[/itex]

Probability: [itex]\left|ψ\right|^{2}d^{3}r[/itex]

Measurement: collapse of ψ - can't assume system possesses properties if not measured

Composite systems: [itex]ψ_{AB} (x_{1},x_{2}) = ψ_{A} (x_{1}) ψ_{B} (x_{2})[/itex] if uncorrelated

I am wondering what (ψ,[itex]\varphi[/itex]) = [itex]\int d^{3}r ψ^{*}(r)\varphi(r)[/itex] means and why it is shown under 'state'.

Any help would be greatly appreciated.

**Copenhagen QM**- classical-quantum divisionState: wavefunction ψ(x); (ψ,[itex]\varphi[/itex]) = [itex]\int d^{3}r ψ^{*}(r)\varphi(r)[/itex]

Evolution: TDSE

Observables ([itex]\hat{x},\hat{p},\hat{H}[/itex]): A = A-dagger; {x,p} = 1 [itex]\rightarrow[/itex] [itex][\hat{x},\hat{p}][/itex] = i[itex]\hbar[/itex]

Probability: [itex]\left|ψ\right|^{2}d^{3}r[/itex]

__Born rule__Measurement: collapse of ψ - can't assume system possesses properties if not measured

Composite systems: [itex]ψ_{AB} (x_{1},x_{2}) = ψ_{A} (x_{1}) ψ_{B} (x_{2})[/itex] if uncorrelated

I am wondering what (ψ,[itex]\varphi[/itex]) = [itex]\int d^{3}r ψ^{*}(r)\varphi(r)[/itex] means and why it is shown under 'state'.

Any help would be greatly appreciated.

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