scholarly journals Noncommutative determinants, Cauchy-Binet formulae, and Capelli-type identities II. Grassmann and quantum oscillator algebra representation

2014 ◽  
Vol 1 (1) ◽  
pp. 1-46 ◽  
Author(s):  
Sergio Caracciolo ◽  
Andrea Sportiello
Keyword(s):  
Quantum Oscillator ◽  
Oscillator Algebra ◽  
Algebra Representation

On the representations of quantum oscillator algebra

1992 ◽  
Vol 24 (2) ◽  
pp. 147-153 ◽  
Author(s):  
Guy Rideau
Keyword(s):  
Quantum Oscillator ◽  
Oscillator Algebra

scholarly journals Discretized representations of harmonic variables by bilateral Jacobi operators

2000 ◽  
Vol 4 (4) ◽  
pp. 297-308
Author(s):  
Andreas Ruffing
Keyword(s):  
Quantum Optics ◽  
Harmonic Oscillator ◽  
Sequence Space ◽  
Heisenberg Algebra ◽  
Harmonic Oscillators ◽  
Quantum Oscillator ◽  
Oscillator Algebra ◽  
Jacobi Operators ◽  
Quantum Properties ◽  
Weighted Sequence Space

Starting from a discrete Heisenberg algebra we solve several representation problems for a discretized quantum oscillator in a weighted sequence space. The Schrödinger operator for a discrete harmonic oscillator is derived. The representation problem for aq-oscillator algebra is studied in detail. The main result of the article is the fact that the energy representation for the discretized momentum operator can be interpreted as follows: It allows to calculate quantum properties of a large number of non-interacting harmonic oscillators at the same time. The results can be directly related to current research on squeezed laser states in quantum optics. They reveal and confirm the observation that discrete versions of continuum Schrodinger operators allow more structural freedom than their continuum analogs do.

Rosen-Chambers Variation Theory of Linearly-Damped Classic and Quantum Oscillator

2014 ◽  
Vol 4 (1) ◽  
pp. 404-426
Author(s):  
Vincze Gy. Szasz A.
Keyword(s):  
Harmonic Oscillator ◽  
Classical Mechanics ◽  
Universal Time ◽  
Variation Theory ◽  
Quantum Oscillator ◽  
Variation Principle ◽  
Poisson Brackets ◽  
Mathematical Meaning ◽  
Damped Harmonic Oscillator ◽  
Damped Oscillator

Phenomena of damped harmonic oscillator is important in the description of the elementary dissipative processes of linear responses in our physical world. Its classical description is clear and understood, however it is not so in the quantum physics, where it also has a basic role. Starting from the Rosen-Chambers restricted variation principle a Hamilton like variation approach to the damped harmonic oscillator will be given. The usual formalisms of classical mechanics, as Lagrangian, Hamiltonian, Poisson brackets, will be covered too. We shall introduce two Poisson brackets. The first one has only mathematical meaning and for the second, the so-called constitutive Poisson brackets, a physical interpretation will be presented. We shall show that only the fundamental constitutive Poisson brackets are not invariant throughout the motion of the damped oscillator, but these show a kind of universal time dependence in the universal time scale of the damped oscillator. The quantum mechanical Poisson brackets and commutation relations belonging to these fundamental time dependent classical brackets will be described. Our objective in this work is giving clearer view to the challenge of the dissipative quantum oscillator.

On models of certain p,q-algebra representations: The p,q-oscillator algebra

2008 ◽  
Vol 49 (5) ◽  
pp. 053504 ◽  
Author(s):  
Vivek Sahai ◽  
Sarasvati Yadav
Keyword(s):  
Oscillator Algebra

scholarly journals Models of q‐algebra representations: Matrix elements of the q‐oscillator algebra

1993 ◽  
Vol 34 (11) ◽  
pp. 5333-5356 ◽  
Author(s):  
E. G. Kalnins ◽  
Willard Miller ◽  
Sanchita Mukherjee
Keyword(s):  
Oscillator Algebra ◽  
Matrix Elements

scholarly journals Hermite Functions and Fourier Series

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 853
Author(s):  
Enrico Celeghini ◽  
Manuel Gadella ◽  
Mariano del Olmo
Keyword(s):  
Fourier Transform ◽  
Hermite Functions ◽  
Quantum Oscillator ◽  
Linear Combinations ◽  
Ladder Operators ◽  
Orthonormal Bases ◽  
Integrable Functions ◽  
The Fourier Transform ◽  
The One ◽  
Square Integrable Functions

Using normalized Hermite functions, we construct bases in the space of square integrable functions on the unit circle (L2(C)) and in l2(Z), which are related to each other by means of the Fourier transform and the discrete Fourier transform. These relations are unitary. The construction of orthonormal bases requires the use of the Gramm–Schmidt method. On both spaces, we have provided ladder operators with the same properties as the ladder operators for the one-dimensional quantum oscillator. These operators are linear combinations of some multiplication- and differentiation-like operators that, when applied to periodic functions, preserve periodicity. Finally, we have constructed riggings for both L2(C) and l2(Z), so that all the mentioned operators are continuous.

Coherent States and the Forced Quantum Oscillator

1965 ◽  
Vol 33 (7) ◽  
pp. 537-544 ◽  
Author(s):  
P. Carruthers ◽  
M. M. Nieto
Keyword(s):  
Coherent States ◽  
Quantum Oscillator

scholarly journals Physical realization of the Glauber quantum oscillator

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
Silvia Gentilini ◽  
Maria Chiara Braidotti ◽  
Giulia Marcucci ◽  
Eugenio DelRe ◽  
Claudio Conti
Keyword(s):  
Quantum Oscillator ◽  
Physical Realization
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