This is an extract from my third year 'Foundations of QM' lecture notes:(adsbygoogle = window.adsbygoogle || []).push({});

If ψ_{1}and ψ_{2}are admissible states,

then the superposed state [itex]\alpha[/itex]ψ_{1}+ ψ_{2}[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.

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# Quantum superposition and Vector Space

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