Re: Coherent states of a superposition

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On Friday, January 18, 2019 at 3:49:10 AM UTC, Brent wrote:
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>
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> On 1/17/2019 5:23 PM, agrays...@gmail.com <javascript:> wrote:
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> On Thursday, January 17, 2019 at 8:33:21 AM UTC, agrays...@gmail.com
> wrote:
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>>
>>
>> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote:
>>>
>>>
>>>
>>> On 1/16/2019 7:25 PM, agrays...@gmail.com wrote:
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>>>
>>>
>>> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
>>>>
>>>>
>>>>
>>>> On 1/13/2019 9:51 PM, agrays...@gmail.com wrote:
>>>>
>>>> This means, to me, that the arbitrary phase angles have absolutely no
>>>> effect on the resultant interference pattern which is observed. But isn't
>>>> this what the phase angles are supposed to effect? AG
>>>>
>>>>
>>>> The screen pattern is determined by *relative phase angles for the
>>>> different paths that reach the same point on the screen*.  The
>>>> relative angles only depend on different path lengths, so the overall
>>>> phase
>>>> angle is irrelevant.
>>>>
>>>> Brent
>>>>
>>>
>>>
>>> *Sure, except there areTWO forms of phase interference in Wave
>>> Mechanics; the one you refer to above, and another discussed in the
>>> Stackexchange links I previously posted. In the latter case, the wf is
>>> expressed as a superposition, say of two states, where we consider two
>>> cases; a multiplicative complex phase shift is included prior to the sum,
>>> and different complex phase shifts multiplying each component, all of the
>>> form e^i (theta). Easy to show that interference exists in the latter case,
>>> but not the former. Now suppose we take the inner product of the wf with
>>> the ith eigenstate of the superposition, in order to calculate the
>>> probability of measuring the eigenvalue of the ith eigenstate, applying one
>>> of the postulates of QM, keeping in mind that each eigenstate is multiplied
>>> by a DIFFERENT complex phase shift.  If we further assume the eigenstates
>>> are mutually orthogonal, the probability of measuring each eigenvalue does
>>> NOT depend on the different phase shifts. What happened to the interference
>>> demonstrated by the Stackexchange links? TIA, AG *
>>>
>>> Your measurement projected it out. It's like measuring which slit the
>>> photon goes through...it eliminates the interference.
>>>
>>> Brent
>>>
>>
>> *That's what I suspected; that going to an orthogonal basis, I departed
>> from the examples in Stackexchange where an arbitrary superposition is used
>> in the analysis of interference. Nevertheless, isn't it possible to
>> transform from an arbitrary superposition to one using an orthogonal basis?
>> And aren't all bases equivalent from a linear algebra pov? If all bases are
>> equivalent, why would transforming to an orthogonal basis lose
>> interference, whereas a general superposition does not? TIA, AG*
>>
>
> *I don't get it. If it's easy to show the existence of interference for a
> general superposition where the components have different phase shifts, why
> would the interference disappear for a special case using orthonormal basis
> components? TIA, AG *
>
>
> But taking the inner product with the *ith* eigenstate is not
> transforming to a different basis.
>
> Brent
>```
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*I know. I meant that from a general superposition used in the
Stackexchange articles, I wrote that general form as a superposition of
eigenstates, and this is where there was an implicit transformation to a
different, specific basis. AG *

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