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I'm a self learner with a decent math background trying to follow this lecture.

I have been able to follow him perfectly up to this point but at 16:00 Professor Balakrishnan states that "<n|a|n> = 0" because |n-1> is perpendicular to |n>. My question is why and how do we know that an energy eigenstate is perpendicular to another energy eigenstate.

-Nate

I have been able to follow him perfectly up to this point but at 16:00 Professor Balakrishnan states that "<n|a|n> = 0" because |n-1> is perpendicular to |n>. My question is why and how do we know that an energy eigenstate is perpendicular to another energy eigenstate.

-Nate

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