Re: Coherent states of a superposition

2019-01-16 Thread Brent Meeker



On 1/16/2019 7:25 PM, agrayson2...@gmail.com wrote:



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

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Re: Coherent states of a superposition

2019-01-16 Thread agrayson2000


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 *

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