Wavefunctions and the indeterminacy principle

Much of what has been said earlier lies at the foundations of the new mechanics which began with the work of the German physicist Max Bom 

In particle diffraction experiments, the probability distribution P(x, t) of the particles, electrons say, in the detector (x coordinate) should be reproduced from a wavefunction ip(x,i). At each value of time, the function P(x, t) is large at values of x where an electron is likely to be found and small at values of x where an electron is unlikely to be found. Using ip x, t) as a probability amplitude function which, to be more general, is allowed to be a complex function, the relation is 

In a double-slit experiment, two functions can be defined, ipi(x,t) and ip2(x, t), for the two possibilities of the electron behaviour, one corresponding to passage through slit 1, the other to slit 2. The appropriate wavefunction 

The last two terms in Eq. (1.16) represent interference. This can be made more clear if the complex functions are written in terms of their magnitudes and phases  

It is easily found that substitution of Eq. (1.17) into Eq. (1.16) leads to  

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