On Application of Unbounded Hilbert Linear Operators in Quantum Mechanics
Eziokwu C. Emmanuel, Bright O. Osu, Iwuanyanwu Vitalis
This research work presents an important Banach space in functional analysis which is known and calledHilbert space. We verified the crucial operations in this space and their applications in physics, particularlyin quantum mechanics. The operations are restricted to the unbounded linear operators densely definedin Hilbert space which is the case of prime interest in physics, precisely in quantum machines. Precisely,we discuss the role of unbounded linear operators in quantum mechanics, particularly, in the study ofHeisenberg uncertainty principle, time-independent Schrodinger equation, Harmonic oscillation, andfinally, the application of Hamilton operator. To make these analyses fruitful, the knowledge of Hilbertspaces was first investigated followed by the spectral theory of unbounded operators, which are claimedto be densely defined in Hilbert space. Consequently, the theory of probability is also employed to studysome systems since the operators used in studying these systems are only dense in H (i.e., they must (orprobably) be in the domain of H defined by L2 ( ) −∞,+∞ ).
•Nov 18, 2020•0 citations