# A Imaginary position operator

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1. Dec 4, 2017

### SeM

Hello, some operators seem to "add up" and give real eigenvalues only if they are applied on the imaginary position, ix, rather than the normal position operator, x, in the integral :

\langle Bx, x\rangle

when replaced by:

\langle Bix, ix\rangle

or

\langle Bix, x\rangle

So using (2) or even (3) I get real (but negative) eigenvalues, instead of complex eigenvalues. I have not found any literature on such an absurd thing, as the imaginary position, however, being the only answer to these operators, I am wondering if anyone can point to some further literature on complex operators and complex eigenvalues in QM and whether (2) and (3) make any sense at all

Thanks

2. Dec 4, 2017

### vanhees71

What's $B$? Without clear definitions, I cannot make any sense of the expressions above. Where does this idea of complex/imaginary position eigenvalues come from?

3. Dec 5, 2017

### SeM

It's an idea that comes from a calculation that sums up only if I use an imaginary position operator. Apparently, it is so non-heard of that I will leave it as it is. It has to do with non-hermiticity, where B (not hermitian) only gives a real value on that integral if the position is imaginary.

Thanks!