The 1D Quantum Oscillator in the Metric Picture

2020 ◽  
pp. 31-53
Author(s):  
Norbert Schwarzer
Keyword(s):  
Quantum Oscillator

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.

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

Dynamics of a composite system in a point source-induced space–time

2021 ◽  
pp. 2150144
Author(s):  
Abdullah Guvendi
Keyword(s):  
Point Source ◽  
Composite System ◽  
Dimensional Space ◽  
Energy Levels ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Space Time ◽  
Spin Coupling ◽  
Quantum Oscillator ◽  
Dimensional Space Time

We investigate the dynamics of a composite system ([Formula: see text]) consisting of an interacting fermion–antifermion pair in the three-dimensional space–time background generated by a static point source. By considering the interaction between the particles as Dirac oscillator coupling, we analyze the effects of space–time topology on the energy of such a [Formula: see text]. To achieve this, we solve the corresponding form of a two-body Dirac equation (fully-covariant) by assuming the center-of-mass of the particles is at rest and locates at the origin of the spatial geometry. Under this assumption, we arrive at a nonperturbative energy spectrum for the system in question. This spectrum includes spin coupling and depends on the angular deficit parameter [Formula: see text] of the geometric background. This provides a suitable basis to determine the effects of the geometric background on the energy of the [Formula: see text] under consideration. Our results show that such a [Formula: see text] behaves like a single quantum oscillator. Then, we analyze the alterations in the energy levels and discuss the limits of the obtained results. We show that the effects of the geometric background on each energy level are not same and there can be degeneracy in the energy levels for small values of the [Formula: see text].

Driving a dissipative quantum oscillator

2018 ◽  
Vol 98 (4) ◽  
Author(s):  
P. C. López Vázquez
Keyword(s):  
Quantum Oscillator

scholarly journals Neutron diffraction investigation of the temperature dependence of crystal structure and thermal motions of red HgI2

2007 ◽  
Vol 63 (6) ◽  
pp. 828-835 ◽  
Author(s):  
Dieter Schwarzenbach ◽  
Henrik Birkedal ◽  
Marc Hostettler ◽  
Peter Fischer
Keyword(s):  
Crystal Structure ◽  
Neutron Diffraction ◽  
Powder Diffraction ◽  
Soft Mode ◽  
Layer Structure ◽  
Neutron Powder Diffraction ◽  
Force Constants ◽  
Quantum Oscillator ◽  
Thermal Displacement ◽  
Tetrahedral Layer

The structure of, and anisotropic thermal motions in, the red semiconductor tetrahedral layer structure of HgI2 have been studied with neutron powder diffraction as a function of temperature from 10 to 293 K. Average thermal displacement parameters U eq of the two atoms are comparable in size at 10 K, but U eq(Hg) increases considerably faster with temperature than U eq(I), the Hg—I bond being highly non-rigid. The anisotropic displacement tensor U (I) is strongly anisotropic with one term about twice as large as the others, while U (Hg) is nearly isotropic. All displacement tensor elements, except U 22(I), increase faster with temperature than harmonic quantum oscillator curves indicating a softening of the isolated-atom potentials at large amplitudes. A lattice dynamical model provides arguments that the anisotropic thermal motions of I are dominated by a soft mode with a wavevector at the [½ ½ 0] boundary of the Brillouin zone consisting essentially of coupled librations of the HgI4 tetrahedra, and by translations of the entire layer. The large vibration amplitudes of Hg suggest weak Hg–I force constants compared with the I–I force constants, allowing Hg to move quite freely inside the tetrahedra. The libration mode induces dynamic deformations of the Hg—I bond with twice its frequency. This provides a mechanism for the anharmonicity and may explain the lightening of the color from red to orange upon cooling at ca 80 K.

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