On 1/16/2019 7:25 PM, [email protected] wrote:
On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote:
On 1/13/2019 9:51 PM, [email protected] <javascript:> 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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