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spaghetti3451
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This is an extract from my third year 'Foundations of QM' lecture notes:
If ψ1 and ψ2 are admissible states,
then the superposed state [itex]\alpha[/itex]ψ1 + ψ2[itex]\beta[/itex] ( [itex]\alpha[/itex],[itex]\beta[/itex] [itex]\in[/itex] C ) is also an admissible state.
[itex]\rightarrow[/itex] complex vector space.
I understand that a linear superposition of allowed state is also an allowed state. It follows from the linearity of the Schrodinger's equation.
What I fail to understand is how this leads to the concept of a complex vector space in QM.
Any help would be greatly appreciated.
If ψ1 and ψ2 are admissible states,
then the superposed state [itex]\alpha[/itex]ψ1 + ψ2[itex]\beta[/itex] ( [itex]\alpha[/itex],[itex]\beta[/itex] [itex]\in[/itex] C ) is also an admissible state.
[itex]\rightarrow[/itex] complex vector space.
I understand that a linear superposition of allowed state is also an allowed state. It follows from the linearity of the Schrodinger's equation.
What I fail to understand is how this leads to the concept of a complex vector space in QM.
Any help would be greatly appreciated.