  The Schr\"odinger theory of electrons in an external electromagnetic field
can be described from the perspective of the individual electron via the
`Quantal Newtonian' laws (or differential virial theorems). These laws are in
terms of `classical' fields whose sources are quantal expectations of Hermitian
operators taken with respect to the wave function. The laws reveal the
following physics: (a) In addition to the external field, each electron
experiences an internal field whose components are representative of a specific
property of the system such as the correlations due to the Pauli exclusion
principle and Coulomb repulsion, the electron density, kinetic effects, and an
internal magnetic field component. (The response of the electron is described
by the current density field.); (b) The scalar potential energy of an electron
is the work done in a conservative field which is the sum of the internal and
Lorentz fields. It is thus inherently related to the properties of the system.
Its constituent property-related components are hence known. It is a known
functional of the wave function; (c) As such the Hamiltonian is a functional of
the wave function, thereby revealing the intrinsic self-consistent nature of
the Schr\"odinger equation. This then provides a path for the determination of
the exact wave function. (d) With the Schr\"odinger equation written in
self-consistent form, the Hamiltonian now admits via the Lorentz field a new
term that explicitly involves the external magnetic field. The new
understandings are explicated for the stationary state case by application to a
quantum dot in a magnetostatic field in both a ground and excited state. For
the time-dependent case, the same states of the quantum dot in both a
magnetostatic and a time-dependent electric field are considered.
