3 research outputs found
Formula for the th -Generalized Fibonacci-like Number
In this paper we provided a formula for the th term of the -generalized
Fibonacci-like sequence, a generalization of the well-known Fibonacci sequence,
having arbitrary initial terms, where the succeeding terms are obtained by
adding its previous terms. The formula for the th term of the
-generalized Fibonacci-like sequence was obtained by observing patterns in
the derived formula for the nth term of the Fibonacci-like, Tribonacci-like,
and Tetrabonacci-like sequence. The formula for the -generalized Fibonacci
sequence was also derived and was used in the process of proving the main
result of this paper
Deformation quantization in the teaching of Lie group representations
In this work, we present straightforward and concrete computations of the unitary irreducible representations of the Euclidean motion group M(2) employing the methods of deformation quantization. Deformation quantization is a quantization method of classical mechanics and is an autonomous approach to quantum mechanics, arising from the Wigner quasiprobability distributions and Weyl correspondence. We advertise the utility and power of deformation theory in Lie group representations. In implementing this idea, many aspects of the method of orbits is also learned, thus further adding to the mathematical toolkit of the beginning graduate student of physics. Furthermore, the essential unity of many topics in mathematics and physics (such as Lie groups and Lie algebras, quantization, functional analysis and symplectic geometry) is witnessed, an aspect seldom encountered in textbooks, in an elementary way