  In his seminal part IV, Ann. der Phys. Vol 81, 1926 paper, Schrodinger has
developed a clear understanding about the wave equation that produces the
correct quadratic dispersion relation for matter-waves and he first presents a
real-valued wave equation that is 4th-order in space and 2nd-order in time. In
view of the mathematical difficulties associated with the eigenvalue analysis
of a 4th-order, differential equation in association with the structure of the
Hamilton-Jacobi equation, Schrodinger splits the 4th-order real operator into
the product of two, 2nd-order, conjugate complex operators and retains only one
of the two complex operators to construct his iconic 2nd-order, complex-valued
wave equation. In this paper we show that Schrodinger's original 4th-order,
real-valued wave equation is a stiffer equation that produces higher energy
levels than his 2nd-order, complex-valued wave equation that predicted with
remarkable success the visible energy levels observed in the visible atomic
line-spectra of the chemical elements. Accordingly, the 4th-order, real-valued
wave equation is too stiff to predict the emitted energy levels from the
electrons of the chemical elements; therefore, the paper concludes that Quantum
Mechanics can only be described with the less stiff, 2nd-order complex-valued
wave equation; unless in addition to the emitted visible energy there is also
dark energy emitted.
