What is the function of a collapsed wave?

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The discussion centers on the concept of wave function collapse in quantum mechanics, particularly in the context of the double-slit experiment. It highlights that the wave function collapses to a specific outcome, such as two lines on a detection screen, which can be described mathematically. The conversation touches on whether this collapse can be defined by a function representing particle behavior rather than wave behavior, and questions the experimental validation of this assumption. The Dirac delta function is mentioned as a relevant mathematical representation in this context. Overall, the collapse of the wave function is crucial for understanding particle behavior in quantum experiments.
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What is the function of a "collapsed" wave?

I know from observing the particle in a dual slit experiment the wave function collapses and the results becomes something like 2 lines, but is there a function that defines the two lines?

Does it just collapse to a function of how the particles would act if they were treated as particles rather than wave-particles? If so, was it experimentally proven, or just assumed?
 
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The wave function 'collapse' of a single particle is a single spot on the screen or film. To see the entire pattern you need more than one photon.

Have you seen an interference pattern from two slits? There is a specific function that depends on wavelength, the distance between the two slits, and the distance to the screen. For a more comprehensive treatment, the width of the slits is also a factor such displayed in the image below.

[PLAIN]http://www.colorado.edu/physics/phys2020/phys2020_f98/lab_manual/Lab5/Image2109.gif
 
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The function is called the dirac delta function.
 
Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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