  The proposed paper presents the unobserved inadequacies in de Broglie's
concepts of wave-particle duality and matter waves in the year 1923. The
commonly admitted quantum energy or frequency expression h{\nu}={\gamma}mc2 is
shown to be inappropriate for matter waves and is acceptable only for photons.
The superluminal phase velocity expression c2/\u{psion}, for matter waves, is
investigated in detail and is also reported to be inadequate. The
rectifications in the inadequate concepts of de Broglie's theory and
refinements in the analogy implementation between light waves and matter waves
are presented, which provides the modified frequency and phase velocity
expression for matter waves. Mathematical proofs for the proposed modified
frequency and phase velocity expression are also presented. In accordance with
the proposed concepts, a wave-particle duality picture is presented which
elucidates the questions coupled with the wave-particle duality, existing in
the literature. Consequently, particle type nature is shown to be a
characteristic of waves only, independent from the presence of matter. The
modifications introduced in the frequency expression for matter waves leads to
variation in the wave function expression for a freely moving particle and its
energy operators, with appropriate justifications. A new relation between the
Kinetic energy and Momentum of the moving body is proposed and is subsequently
applied to introduce novel General and Relativistic Quantum Mechanical Wave
Equations. Applications of these equations in bound state quantum mechanical
systems provide the information regarding particle's general and relativistic
behavior in such systems. Moreover, the proposed wave equations can also be
transformed into Schr\"odinger's and Dirac's equations. The interrelation of
Schr\"odinger's, Dirac's and proposed equations with the universal wave
equation is also presented.
