On 1/17/2019 5:23 PM, [email protected] wrote:
On Thursday, January 17, 2019 at 8:33:21 AM UTC, [email protected] wrote:On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote: 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] 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? AGThe 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.
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