This monograph provides an in-depth analysis of particle kinematics through the lens of a newly proposed semi-classical parameter, Omega Naught. Rather than treating quantum and classical regimes as disparate entities, this work explores the transitionary "granularity" of motion that emerges when reconciling de Broglie’s wave-particle duality with Newtonian force relations. The analysis utilizes the derivation of the v^3 = K*a relation as a primary kinematic signature to test the validity of the Omega Naught framework. Furthermore, the study demonstrates the robustness of this model by applying it to Bohr’s quantization of the Hydrogen atom, showing that such quantum states emerge naturally as geometric consequences of the underlying kinematic constraints. By documenting boundary conditions and velocity-acceleration dynamics over extensive theoretical derivations, this paper establishes Omega Naught as a critical scaling constant for predicting system behavior in the semi-classical regime. The results offer a unified perspective on quantization as an extension of fundamental kinematic evolution.This monograph provides an in-depth analysis of particle kinematics through the lens of a newly proposed semi-classical parameter, Omega Naught. Rather than treating quantum and classical regimes as disparate entities, this work explores the transitionary "granularity" of motion that emerges when reconciling de Broglie’s wave-particle duality with Newtonian force relations. The analysis utilizes the derivation of the v^3 = K*a relation as a primary kinematic signature to test the validity of the Omega Naught framework. Furthermore, the study demonstrates the robustness of this model by applying it to Bohr’s quantization of the Hydrogen atom, showing that such quantum states emerge naturally as geometric consequences of the underlying kinematic constraints. By documenting boundary conditions and velocity-acceleration dynamics over extensive theoretical derivations, this paper establishes Omega Naught as a critical scaling constant for predicting system behavior in the semi-classical regime. The results offer a unified perspective on quantization as an extension of fundamental kinematic evolution.

Apr 14, 20260 citations

Dihedral symmetry of periodic chain: quantization and coherent states

Luft, P, Goce Chadzitaskos, J. Tolar

Our previous work on quantum kinematics and coherent states over finite configuration spaces is extended: the configuration space is, as before, the cyclic group $Z_{n}$ of arbitrary order n=2,3,..., but as its symmetry group a larger group -- the non-Abelian dihedral group $D_{n}$ -- is taken. The corresponding group related coherent states are constructed and their overcompleteness proved. Our approach based on geometric symmetry can be used as a kinematic framework for matrix methods in quantum chemistry of ring molecules.Our previous work on quantum kinematics and coherent states over finite configuration spaces is extended: the configuration space is, as before, the cyclic group $Z_{n}$ of arbitrary order n=2,3,..., but as its symmetry group a larger group -- the non-Abelian dihedral group $D_{n}$ -- is taken. The corresponding group related coherent states are constructed and their overcompleteness proved. Our approach based on geometric symmetry can be used as a kinematic framework for matrix methods in quantum chemistry of ring molecules.

Feb 19, 20070 citations

Dihedral symmetry of periodic chain: quantization and coherent states

P Luft, G Chadzitaskos, J Tolar

Our previous work on quantum kinematics and coherent states over finite configuration spaces is extended: the configuration space is, as before, the cyclic group Z_n of arbitrary order n=2,3,..., but a larger group - the non-Abelian dihedral group D_n - is taken as its symmetry group. The corresponding group related coherent states are constructed and their overcompleteness proved. Our approach based on geometric symmetry can be used as a kinematic framework for matrix methods in quantum chemistry of ring molecules.Our previous work on quantum kinematics and coherent states over finite configuration spaces is extended: the configuration space is, as before, the cyclic group Z_n of arbitrary order n=2,3,..., but a larger group - the non-Abelian dihedral group D_n - is taken as its symmetry group. The corresponding group related coherent states are constructed and their overcompleteness proved. Our approach based on geometric symmetry can be used as a kinematic framework for matrix methods in quantum chemistry of ring molecules.

arXiv:quant-ph/0702180Journal of Physics A Mathematical and TheoreticalApr 17, 20070 citations

Our previous work on quantum kinematics and coherent states over finite configuration spaces is extended: the configuration space is, as before, the cyclic group

Z_{n}

of arbitrary order n=2,3,..., but as its symmetry group a larger group -- the non-Abelian dihedral group

D_{n}

-- is taken. The corresponding group related coherent states are constructed and their overcompleteness proved. Our approach based on geometric symmetry can be used as a kinematic framework for matrix methods in quantum chemistry of ring molecules.