The Harmonic Oscillator
The group theory of the harmonic oscillator with applications in physics
... in quantum field theory.. The use of the transition group to describe the harmonic oscillator was found to be of considerable use in the calcul- ation of matrix [r] ...
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Isothermal quantum dynamics: Investigations for the harmonic oscillator
... However, the present development stage of the method does not yet permit the investiga- tion of quantum systems other than the harmonic oscillator that are not solvable with more traditional methods. It is ...
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The Harmonic Oscillator with Random Damping in Non Markovian Thermal Bath
... the harmonic oscillator with random damping in non-Markovian thermal ...damped harmonic oscillator with multiplicative colored noise and translate it into the additive colored noise by ...
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The Harmonic Oscillator
... The second method, called the ladder or algebraic method, does not deal with solving the Schr¨ odinger equation, but deals instead with operator algebra involving operators known as the [r] ...
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Kinematical Brownian Motion of the Harmonic Oscillator in Non-Commutative Space
... Abstract: In this work the Jacobi’s second equality in the form of stochastic equation and the Wiener path integral approach are used to evaluate the probability density of harmonic oscillator in ...
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The Quantum Harmonic Oscillator Stephen Webb
... The harmonic oscillator also gives the exact solution for a particle in a uniform magnetic field of a given vector potential, as that vector potential merely takes the form of a two-dimensional ...
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Quantum dynamics of the damped harmonic oscillator
... damped harmonic oscillator has been a subject of continual investigation since the ...additional harmonic oscillators as a ...the oscillator of ...the harmonic oscillator with ...
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FLAP P11.2 The quantum harmonic oscillator
... the harmonic oscillator in the realm of classical or large- scale physics, and then go on to study the harmonic oscillator in the quantum or microscopic ...the harmonic ...
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PARALLEL IMPLEMENTATION OF THE COUPLED HARMONIC OSCILLATOR
... harmonic oscillator. From the analytical solution of the coupled harmonic oscillator, the design parameters are ...the harmonic oscillator ...
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Maximal Regularity of the Discrete Harmonic Oscillator Equation
... The paper is organized as follows. The second section provides the definitions and preliminary results to be used in the theorems stated and proved in this work. In particular to facilitate a comprehensive understanding ...
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The Collatz Conjecture and the Quantum Mechanical Harmonic Oscillator
... QM harmonic oscillator eigenstates (bits), the latter linear differential equations can be decomposed themselves into an even larger set of linear differential equa- tions involving the harmonic ...
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Harmonic Oscillator SUSY Partners and Evolution Loops
... . 6 Conclusions In this paper it has been shown that the SUSY partners of the harmonic oscillator Hamiltonian realize straightforwardly the polynomial Heisenberg algebras of order 2k. As a consequence, if ...
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On simulations of the classical harmonic oscillator equation by difference equations
... where ε is a constant. The continuum limit (1.3) yields, in any of these cases, the harmonic oscillator equation x ¨ + x = 0. (2.4) To fix our attention, in this paper we consider only the solutions ...
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On the Cauchy problem for a linear harmonic oscillator with pure delay
... the harmonic oscillator, has a two-dimensional eigenspace so that the solution of the homogeneous problem can be written as a linear combination of these two ...linear oscillator with pure ...
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Quantization of Harmonic Oscillator Soliton by Friction Term Method
... the harmonic oscillator comprises one of the most important examples of elementary Quantum ...linear harmonic oscillator describes vibrations in molecules and their counterparts in solids, the ...
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2. Simple harmonic oscillator driven by an impulse force
... The harmonic oscillator is famously used among many systems to model the motion of a mass-spring ...driven harmonic oscillator is known as a simple harmonic ...simple harmonic ...
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The Two-dimensional Harmonic Oscillator on a Noncommutative Space with Minimal Uncertainties
... E-mail: [email protected], [email protected] A : The two dimensional set of canonical relations giving rise to minimal uncer- tainties previously constructed from a q-deformed oscillator algebra is further ...
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Describe a Bell and Breathe Solitons by Using Harmonic Oscillator Soliton
... the harmonic oscillator comprises one of the most important examples of elementary Quantum ...linear harmonic oscillator describes vibrations in molecules and their counterparts in solids, the ...
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Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials
... quantum harmonic oscillator that is exactly solvable by polynomials is monodromy free, and therefore can be obtained by applying a finite number of state-deleting Darboux transformations on the ...
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Delay Harmonic Oscillator
... t = = = (27) 4. Conclusions In this paper, the propagation delay of a deformation traveling through the spring is considered, and therefore, is called the Delay Harmonic Oscillator. The Equations of Motion ...
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