# Re: Coherent states of a superposition

```
On Wednesday, December 5, 2018 at 11:42:06 AM UTC, agrays...@gmail.com
wrote:
>
>
>
> On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:
>>
>> On Wed, Dec 5, 2018 at 2:36 AM <agrays...@gmail.com> wrote:
>>
>>>
>>> *Thanks, but I'm looking for a solution within the context of
>>> interference and coherence, without introducing your theory of
>>> consciousness. Mainstream thinking today is that decoherence does occur,
>>> but this seems to imply preexisting coherence, and therefore interference
>>> among the component states of a superposition. If the superposition is
>>> expressed using eigenfunctions, which are mutually orthogonal -- implying
>>> no mutual interference -- how is decoherence possible, insofar as
>>> coherence, IIUC, doesn't exist using this basis? AG*
>>>
>>
>> I think you misunderstand the meaning of "coherence" when it is used off
>> an expansion in terms of a set of mutually orthogonal eigenvectors. The
>> expansion in some eigenvector basis is written as
>>
>>    |psi> = Sum_i (a_i |v_i>)
>>
>> where |v_i> are the eigenvectors, and i ranges over the dimension of the
>> Hilbert space. The expansion coefficients are the complex numbers a_i.
>> Since these are complex coefficients, they contain inherent phases. It is
>> the preservation of these phases of the expansion coefficients that is
>> meant by "maintaining coherence". So it is the coherence of the particular
>> expansion that is implied, and this has noting to do with the mutual
>> orthogonality or otherwise of the basis vectors themselves. In decoherence,
>> the phase relationships between the terms in the original expansion are
>> lost.
>>
>> Bruce
>>
>
> I appreciate your reply. I was sure you could ascertain my error --
> confusing orthogonality with interference and coherence. Let me have your
> indulgence on a related issue. AG
>```
```
Suppose the original wf is expressed in terms of p, and its superposition
expansion is also expressed in eigenfunctions with variable p. Does the
phase of the original wf carry over into the eigenfunctions as identical
for each, or can each component in the superposition have different phases?
I ask this because the probability determined by any complex amplitude is
independent of its phase. TIA, AG

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