Third-order constants of motion in quantum mechanics

1977 ◽  
Vol 16 (11) ◽  
pp. 829-835 ◽  
Author(s):  
S. Datta Majumdar ◽  
M. J. Englefield
Keyword(s):  
Quantum Mechanics ◽  
Third Order ◽  
Constants Of Motion

QUANTIZATION OF CLASSICAL CONSTANTS OF MOTION AND EQUILIBRIUM DISTRIBUTIONS IN QUANTUM MECHANICS

1996 ◽  
Vol 10 (15) ◽  
pp. 723-730
Author(s):  
Z. HABA
Keyword(s):  
Quantum Mechanics ◽  
Statistical Mechanics ◽  
Quantum Statistical Mechanics ◽  
Quantum Systems ◽  
Quantization Procedure ◽  
Constant Of Motion ◽  
Additional Constant ◽  
Constants Of Motion ◽  
Equilibrium Distributions ◽  
Quantum Statistical

We distinguish a class of quantum systems (trigonometric and hyperbolic potentials) with an additional constant of motion unrelated to any symmetry. The various quantum constants of motion result from non-uniqueness of the quantization procedure. We discuss equilibrium distributions in quantum statistical mechanics determined by the constants of motion.

Testing quantum mechanics using third-order correlations

1996 ◽  
Vol 53 (4) ◽  
pp. 2000-2008 ◽  
Author(s):  
Paul Kinsler
Keyword(s):  
Quantum Mechanics ◽  
Third Order

scholarly journals Noether symmetries, dynamical constants of motion, and spectrum generating algebras

2021 ◽  
Vol 36 (24) ◽  
pp. 2150166
Author(s):  
Daddy Balondo Iyela ◽  
Jan Govaerts
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Time Derivative ◽  
Hamiltonian Formulation ◽  
Lie Symmetry ◽  
Noether Symmetries ◽  
Time Dependency ◽  
Converse Statement ◽  
Constants Of Motion ◽  
Total Time Derivative

When discussing consequences of symmetries of dynamical systems based on Noether’s first theorem, most standard textbooks on classical or quantum mechanics present a conclusion stating that a global continuous Lie symmetry implies the existence of a time-independent conserved Noether charge which is the generator of the action on phase space of that symmetry, and which necessarily must as well commute with the Hamiltonian. However this need not be so, nor does that statement do justice to the complete scope and reach of Noether’s first theorem. Rather a much less restrictive statement applies, namely, that the corresponding Noether charge as an observable over phase space may in fact possess an explicit time dependency, and yet define a constant of the motion by having a commutator with the Hamiltonian which is nonvanishing, thus indeed defining a dynamical conserved quantity. Furthermore, and this certainly within the Hamiltonian formulation, the converse statement is valid as well, namely, that any dynamical constant of motion is necessarily the Noether charge of some symmetry leaving the system’s action invariant up to some total time derivative contribution. This contribution revisits these different points and their consequences, straightaway within the Hamiltonian formulation which is the most appropriate for such issues. Explicit illustrations are also provided through three general but simple enough classes of systems.

scholarly journals Hyperconfluent third-order supersymmetric quantum mechanics

2011 ◽  
Vol 44 (36) ◽  
pp. 365302 ◽  
Author(s):  
David J Fernández C ◽  
Encarnación Salinas-Hernández
Keyword(s):  
Quantum Mechanics ◽  
Supersymmetric Quantum Mechanics ◽  
Third Order
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