The densities of a subatomic particle

It seems to be pretty generally accepted today that all that we can
ever know about the structure of a subatomic particle is implicit in
the particle's wave function and with the right mathematical tools can
be extracted from it. A classical physicist such as Einstein would
see the first priority in describing the structure of a particle as
that of providing equations defining the distribution of its charge,
current and mass-energy, ie a set of densities, and would expect the
Standard Model to be able to produce them.

In the quantum mechanics of eighty years ago, Segre ("From X-Rays to
Quarks", 1980, p 163) writes: "However, there was a big unsolved
question. What is the psi, the mysterious field scalar that propagates
as a wave? For some time Schrodinger and others thought that the square
of the modulus of the complex number psi was the density of electric
charge, as if the electron dissolved itself into a cloud." Heisenberg
("The Physical Principles of the Quantum Theory", 1930, p 161) spelled
this assumption out, including with it matching equations for current
density and mass energy density and showed that the conservation laws
were satisfied by these definitions.

Can the Standard Model provide an equivalent set of equations defining
these densities, a set that is intelligible to an undergraduate? If
not, why not?

Phil Gardner

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