Operation on complex conjugate

[Thejas15101998]

Why do we sandwich operators in quantum mechanics in such a way that the operator acts on the wavefunction and not on its complex conjugate?

 

[PeroK]

Why do we sandwich operators in quantum mechanics in such a way that the operator acts on the wavefunction and not on its complex conjugate?

You could define things the other way round. In fact, using the "mathematician's" definition of an inner product would probably have things that way round. All the results would be the same.

See, for example:

https://en.wikipedia.org/wiki/Inner_product_space

 

[Strilanc]

As a follow-up on what PeroK said, note that it is important that you can only do one. If you can operate on a wavefunction and also on that wavefunction's conjugate (or, equivalently, if you're given an operation that can conjugate the wavefunction), it becomes possible to send information faster than light.