wave function of double Slit experiment

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For example, if the (one dimensional) position of a particle consisted of a normal statistical distribution with a mean position of 0m and a variance of 1 at time t = 0, it’s wave function would be:

So, applying this to the twin slit experiment:

if

and

then:

ne of the major ramifications of the statistical interpretation is that it can be (and is) used as a mathematical model of particles at the subatomic level. Thus, the mathematical manipulation of particles is possible, much like in the classical domain. For example, classically:

Then, by using operators (which manipulate a wave function to produce a probability distribution of a particular aspect of the particle), a statistical equivalent is developed:

Advantages of the Statistical Ensemble Interpretation

The Statistical Model has the added advantage of being able to avoid any ‘half dead, half alive’ cat states.
The question about what state the cat is in – has been asked so many times, that people take for granted that it is a valid question.
While the question may be valid, QM never provided any means for answering the question.
If we go with the statistical ensemble interpretation, the only things we can ask about the state of the system – are the probabilities of the various OUTCOMES. Outcomes implies measurement. Hence,

 

Check out also – Problems In Advanced Math and Physics and Rare Finds in Special and General Relativity