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I'm currently studying second quantization. I need to prove [itex]<n^\prime| n>=\delta_{n^\prime n}[/itex] by mathematical induction in the number of particles representation. However I don't know how to do this proof having two natural numbers [itex]n[/itex] and [itex]n^\prime[/itex]. Must I prove it holds for [itex]<0|0>[/itex], [itex]<0|1>[/itex] and [itex]<1|1>[/itex]. Then assuming it holds true for [itex]<n^\prime|n>[/itex], prove it for [itex]<n^\prime|n+1>[/itex] and [itex]<n^\prime +1|n+1>[/itex]. Excuse me if this is an obvious question, please help me.

Thanks a lot.

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# Orthogonality by Induction

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