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The Quantum Harmonic Oscillator
2018The oscillator Hamiltonian in the coordinate representation is: $$\hat{H} = {p^{2} \over 2m} +\frac{1}{2} m \omega ^{2} x^{2}.$$
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The Quantum Mechanical Harmonic Oscillator
1988In Chap. 5 we have treated one-dimensional harmonic and anharmonic oscillations. The harmonic oscillation was characterised by the fact that the oscillation frequency did not depend on the amplitude of the displacement. If we had considered three-dimensional motion we should have found that for the harmonic oscillator all circular and elliptical orbits
Erich W. Schmid +2 more
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The quantum harmonic oscillator on a lattice
Journal of Physics A: Mathematical and General, 1986The authors find the eigenvalue spectrum of a particle constrained to 'hop' between the sites of a simple cubic lattice in the presence of a spherically asymmetric 'harmonic oscillator' potential. The eigenfunctions are found to be given in terms of the periodic Mathieu functions of period pi .
J. P. Gallinar, G Mata, E R Chalbaud
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Quantum-Mechanical Harmonic Oscillator
2018Quantum-mechanical treatment of a harmonic oscillator has been a well-studied topic from the beginning of the history of quantum mechanics. This topic is a standard subject in classical mechanics as well. In this chapter, first we briefly survey characteristics of a classical harmonic oscillator.
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A novel digital contents privacy scheme based on quantum harmonic oscillator and schrodinger paradox
Wirel. Networks, 2020Abdullah A. Alghafis +5 more
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Quantum Harmonic Oscillator and Schrodinger Paradox Based Nonlinear Confusion Component
International Journal of Theoretical Physics, 2020Sundas Tariq +3 more
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Measuring the quantum harmonic oscillator
Frontiers in Optics 2010/Laser Science XXVI, 2010By coupling a superconducting quantum bit to microwave electromagnetic and mechanical resonators, we can demonstrably achieve the resonators’ quantum ground states, and create photon and phonon Fock states, and arbitrary superpositions of photon Fock states.
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Quantum Theory of Harmonic Oscillator [PDF]
, 2010 The quantum theory of the harmonic oscillator is of particular importance for many reasons. In fact, harmonic forces are often present in nature and even more often used as model systems. Small oscillations about a point of stable equilibrium are described as independent harmonic oscillators, as we have seen in sect. 1.5.
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Quantum Harmonic Oscillation and the quantum Multiverse
Introduces structured quantum oscillations at a universal level. The first serious discussion of Multiverse as harmonic oscillators.Hilmir Frímann Halldórsson +2 more
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Foundations of Quantum Mechanics—The Harmonic Oscillator [PDF]
, 1979 This chapter, the longest in the book, introduces three of the basic assumptions of quantum mechanics and then illustrates them, using mainly the example of the harmonic oscillator. Though some historic remarks are included, neither the historic development nor any other heuristic way towards quantum mechanics is followed.
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