tag:blogger.com,1999:blog-9074529824943791718.post8170148800647306214..comments2009-10-30T09:03:13.951-04:00Bryanhttp://www.blogger.com/profile/07379669532781325751noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-9074529824943791718.post-16311327012891689672009-10-05T02:11:19.521-04:002009-10-05T02:11:19.521-04:00Except that the wave function can have magnitude greater than 1 at a given point, as long as that region is small enough. So it can go anywhere with respect to the dial.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-9074529824943791718.post-72227491611037624802009-10-05T01:43:51.149-04:002009-10-05T01:43:51.149-04:00Thanks -- I was a bit too quick with this idea.<br /><br />I believe it would have been better to say that the contribution of <em>histories</em> to amplitudes can be thought of in my way: a path contributes exp(iS) to the total amplitude of an event (S=action along the path). And exp(iS) is just a reading on my meter.<br /><br />But for where I&#39;m going with this next time (visualizing time reversal), there&#39;s a more informative way to fix up my idea. Just take <b>little finite regions instead of points</b>. And think of ψ as assigning to each little region a complex number <em>properly inside</em> the unit circle -- i.e., in the picture, <b>the arrow on the dial can move in and out as well as around</b>, never touching the edge of the circle. Then you can normalize, and recover the usual description of the wave function. And then you can describe useful things like hydrogen atoms and harmonic oscillators that no one wants to do without, too.<br /><br />I&#39;ll make a note of this in the post text. Thanks again.Bryanhttp://www.blogger.com/profile/07379669532781325751noreply@blogger.comtag:blogger.com,1999:blog-9074529824943791718.post-87880175928786163692009-10-05T00:13:37.813-04:002009-10-05T00:13:37.813-04:00Big problem - the overall wave function has unit length, but the wave function at any given point does not. You couldn&#39;t normalize any wave function properly if your description were accurate - at best you could &quot;normalize to the delta function.&quot; psi*psi is the probability density and also the length square of the complex number you claim is unity. Some examples of real world wave functions which fail your description:<br />hydrogen atom,<br />harmoic oscillator,<br />bound states of the various square wells,<br />etc.<br /><br />I think you&#39;re confusing the path integral description of what you add up with the final wave function.Anonymousnoreply@blogger.com