scholarly journals Converting translation operators into plane polar and spherical coordinates and their use in determining quantum-mechanical wavefunctions in a representation-independent fashion

2021 ◽  
Vol 62 (7) ◽  
pp. 072102
Author(s):  
Michael Rushka ◽  
M. A. Esrick ◽  
W. N. Mathews ◽  
J. K. Freericks
Keyword(s):  
Quantum Mechanical ◽  
Spherical Coordinates ◽  
Translation Operators

scholarly journals Gauge-Independent Theory of Symmetry. II.

1965 ◽  
Vol 18 (2) ◽  
pp. 109 ◽  
Author(s):  
HA Buchdahl ◽  
LJ Tassie
Keyword(s):  
Relativistic Quantum ◽  
Classical Mechanics ◽  
Equation Of Motion ◽  
Symmetry Operation ◽  
Quantum Mechanical ◽  
Translation Invariant ◽  
Translation Operators ◽  
Physical Symmetry ◽  
Magnetic Translation ◽  
Quantum Mechanical Systems

This paper develops a gauge-independent symmetry theory of non-relativistic quantum mechanical systems, in line with that previously considered in the context of classical mechanics. We first discuss at length the motivation for adopting the view that the invariance of a system K under a physical symmetry operation .<I' should be taken to mean invariance of the equation of motion of K under a certain gauge-independent unitary transformation U c( .<1'). The formal development of the theory is then carried through, and some detailed examples are presented. In particular, corresponding to every direction along which a system K happens to be translation invariant there exists a gauge-independent generator of translations which leaves K invariant but which is not, in general, a component of either the canonical or the kinetic momentum. The connexion between such invariant generators of translations and the so-called magnetic translation operators is referred to.

Operators and meaning of wave function

2016 ◽  
pp. 4039-4042
Author(s):  
Viliam Malcher
Keyword(s):  
Wave Function ◽  
Quantum Theory ◽  
State Vector ◽  
The State ◽  
Physical Significance ◽  
Central Problem ◽  
Quantum Mechanical ◽  
Mechanical Description ◽  
Quantum Mechanical Description ◽  
Interpretation Of Quantum Theory

The interpretation problems of quantum theory are considered. In the formalism of quantum theory the possible states of a system are described by a state vector. The state vector, which will be represented as |ψ> in Dirac notation, is the most general form of the quantum mechanical description. The central problem of the interpretation of quantum theory is to explain the physical significance of the |ψ>. In this paper we have shown that one of the best way to make of interpretation of wave function is to take the wave function as an operator.

Optical and Electrical Properties of Organic Conducting Polymers

2014 ◽  
Vol 8 (1) ◽  
pp. 1457-1463
Author(s):  
Salah Abdulla Hasoon
Keyword(s):  
Electrical Properties ◽  
Conjugated Polymer ◽  
Polymeric Materials ◽  
Quantum Mechanical ◽  
Optical And Electrical Properties ◽  
Electrically Conducting ◽  
Temperature Ranges ◽  
Lithium Tetrafluoroborate ◽  
Absorbance Peak ◽  
Polymerization Method

Novel electrically conducting polymeric materials are prepared in this work. Polythiophene (PT) and poly (3-Methelthiophene) (P3MT) films were prepared by electro-polymerization method using cyclic voltammetry in acetonitrile as a solvent and lithium tetrafluoroborate as the electrolyte on a gold electrode. Electrical properties of P3MT have been examined in different environments using UV-Vis absorption spectroscopy and quantum mechanical ab initio calculations, The observed absorption peaks at 314 and 415 nm, were attributed to the n-π* and π-π* transitions, respectively in the conjugated polymer chain, in contrast, the observed absorbance peak at 649 nm, is responsible for electric conduction. The temperature dependence of the conductivity can be fitted to the Arrhenius and the VTF equations in different temperature ranges.

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