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Quantum solutions of the damped harmonic oscillator
American Journal of Physics, 1983Solutions to the Fokker–Planck equation for a damped harmonic oscillator corresponding to uniquely quantum-mechanical initial states with no classical correspondence are given.
G J Milburn, Walls D F
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The Quantum Harmonic Oscillator
2023Abstract We consider the time-independent Schrödinger equation for the harmonic oscillator potential and determine its bound states and energy levels in one spatial dimension using two approaches: the algebraic and the analytic method. Using the former, we introduce ladder operators: the annihilation and creation operators, as well as ...
Reinhold A. Bertlmann, Nicolai Friis
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Quantum harmonic oscillator with superoscillating initial datum [PDF]
Journal of Mathematical Physics, 2014 In this paper, we study the evolution of superoscillating initial data for the quantum driven harmonic oscillator. Our main result shows that superoscillations are amplified by the harmonic potential and that the analytic solution develops a singularity ...
Fabrizio Colombo +2 more
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Linear chaos in the quantum harmonic oscillator
Journal of Systems Science and Complexity, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xinxing Wu, Peiyong Zhu
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Quantum theory of the damped harmonic oscillator
Physical Review A, 1990The quantum theory of a damped harmonic oscillator is developed by considering an exactly solvable model, previously discussed by Unruh and Zurek [Phys. Rev. D 40, 1071 (1989)]. A one-dimensional harmonic oscillator is coupled to a scalar field. The field is assumed to be initially in thermal equilibrium.
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Harmonic oscillator driven by a quantum current
Physical Review Letters, 1989We show that under certain circumstances a simple quantum harmonic oscillator driven by a quantum current evolves to unique pure states even if started as a mixed state. In various limits, these states exhibit nonclassical properties such as sub-Poissonian statistics, or more interestingly resemble macroscopic superpositions.
, Slosser, , Meystre, , Braunstein
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Dissipation in Quantum Mechanics. The Harmonic Oscillator
Physical Review, 1960The need for a quantum-mechanical formalism for systems with dissipation which is applicable to the radiation field of a cavity is discussed. Two methods that have been used in this connection are described. The first, which starts with the classical Newtonian equation of motion for a damped oscillator and applies the conventional formal quantization ...
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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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A Note on the Quantum Rule of the Harmonic Oscillator
Physical Review, 1951The purpose of the present note is to show, with the aid of an elementary example, that the commutation rules, which are usually given the rule of postulates in quantum mechanics, are in fact not arbitrary, provided that a more stringent definition of the Hilbert space and a strict expansion theorem are adopted.
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