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we always listen to the phrase in quantum mechanics textbook that says this eigenvector is unique to within a constant factor.

What does it actually mean?

unique means there is one and only one??

constant factor: a constant 2 or 3 or... maybe??

I don't really catch the physical picture of it, I just hope for some mathematical examples that can illustrate this. Thank you

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# Unique to within a constant factor?

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