| dc.description.abstract | Operators in Hilbert space have properties which are useful in the study of mathematical abstract
areas such as approximation theory, Banach Fixed point theory, the spectral theory as
well as Quantum Mechanics. Schrödinger equation is a fundamental entity with many applications
in Quantum Mechanics. This equation was initially derived by applying the knowledge
of electromagnetic wave function and Einstein theory of relativity. Later, it was derived by
applying the knowledge of Newtonian mechanics. It was also derived by extending the wave
equation for classical fields to photons and simplified using approximations consistent with
generalized non-zero rest mass. However, from the existing literature no study has been done
on deriving Schrödinger equation using properties of Hilbert space operators. In this study,
Hilbert space operators that include unitary operators, self adjoint operators and compact operators,
norms of linear operators, Hilbert Schmidt operator, normal operators together with
Lebesque Integral, Neumann Integral and spectrum are used in place of the existing concepts
of electromagnetic wave function, Einstein theory of relativity and approximation consistent
with generalized non zero mass to derive the Schrödinger equation. Furthermore, this study
has established the correlation between the electromagnetic wave function and Einstein theory
of relativity in relation with Hilbert space operators. Application of Hilbert space operators
on Quantum observables such as position, momentum and energy of a particle has been done
in these study. The derivation of Schrödinger enhances equation and its application using
Hilbert space operators have enhanced a better understanding of the concept of Schrödinger
equation. The results of this work will be useful in quantum mechanics as well as in mathematical
operator theory. | en_US |
