A true wavefunction y(r,t) of quantum mechanics (QM) can be singly, doubly, or multiply argumentative depending on the explicit or implicit occurrence of its arguments (independent variables of the function): the position vector r and the free parameter of time, t. There is a probable ambiguity which has been partially removed where and when y(r,t) is expressed as complex numbers. Complete removal requires real arguments. Nonetheless, the time parameter will always remain the real part of the complex imaginary argument as product of the phase factor where and when the position vector now describes a radius vector of the complex plane and positive phase angle q is counterclockwise with respect to the real axis as the principal reference. Angle q is negative if measured clockwise.
Furthermore, the argumentative wavefunctions of QM must all be well behaved. That is to say a wavefunction should be well defined and must be continuous everywhere and everywhen in spacetime. It must be differentiable and single valued. Last but not least, it must be square-integrable; meaning its integral from negative infinity to positive infinity of its square modulus must be finite. Furthermore, where and when this integral of modulus square was normalized by Max Born (1882-1970) in 1926 and he defined it as the probability density wavefunction, together with Walther Bothe’s “Coincidence Method” the usefulness without any arguments led them to share the 1954 Nobel Prize for physics.


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