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Let a system consist of two particles A and B and let their wave-fuctions by ψa and ψb respectively..Let ψc represent the wavefuction of the system..

In this book, it is given that

ψc is a product of ψa and ψb..

How is this possible?

We have learnt about the probability of existence of a particle by integrating the wave-function..Does this concept have anything to do with the wavefunction of the system..

Please explain me in an intuitive way without tough mathematics..