Current Density Probability Conservation Theorem

THEOREM Schrddinger equation is compatible with charge conservation at the probability density level. 

Firstly, let s unfold the meaning of conservation at the probability density level in an analytical manner that is considering a certain volume region of the space, say Tj, that is characterized by the localization density probability 

Quantum Nanochemistry-Volume I Quantum Theory and Observability 

their subtraction firstly leads with expression  

Finally, there is remarkable that the current density probability current has as one of its major consequences the property of wave functions to be square integrable, i.e., with finite constant value for the integral 

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