On Saturday, December 8, 2018 at 2:46:41 PM UTC, agrays...@gmail.com wrote:
>
>
>
> On Thursday, December 6, 2018 at 5:46:13 PM UTC, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Wednesday, December 5, 2018 at 10:13:57 PM UTC, agrays...@gmail.com 
>> wrote:
>>>
>>>
>>>
>>> On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote:
>>>>
>>>> On Wed, Dec 5, 2018 at 10:52 PM <agrays...@gmail.com> wrote:
>>>>
>>>>> 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 
>>>>>
>>>>
>>>> The phases of the coefficients are independent of each other.
>>>>
>>>
>>> When I formally studied QM, no mention was made of calculating the 
>>> phases since, presumably, they don't effect probability calculations. Do 
>>> you have a link which explains how they're calculated? TIA, AG 
>>>
>>
>> I found some links on physics.stackexchange.com which show that relative 
>> phases can effect probabilities, but none so far about how to calculate any 
>> phase angle. AG 
>>
>
> Here's the answer if anyone's interested. But what's the question? How are 
> wf phase angles calculated? Clearly, if you solve for the eigenfunctions of 
> some QM operator such as the p operator, any phase angle is possible; its 
> value is completely arbitrary and doesn't effect a probability calculation. 
> In fact, IIUC, there is not sufficient information to solve for a unique 
> phase. So, I conclude,that the additional information required to uniquely 
> determine a phase angle for a wf, lies in boundary conditions. If the 
> problem of specifying a wf is defined as a boundary value problem, then, I 
> believe, a unique phase angle can be calculated. CMIIAW. AG 
>
>>
>>>> Bruce
>>>>
>>>
I could use a handshake on this one. Roughly speaking, if one wants to 
express the state of a system as a superposition of eigenstates, how does 
one calculate the phase angles of the amplitudes for each eigenstate? AG

>
>>>>  
>>>>
>>>

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