Results 291 to 300 of about 162,690 (325)

The Quantum Mechanical Harmonic Oscillator

1988
In 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, Gerhard Spitz, Wolfgang Lösch   +2 more
openaire   +2 more sources

Hyperincursive Algorithms of Classical Harmonic Oscillator Applied to Quantum Harmonic Oscillator Separable Into Incursive Oscillators

, 2015
This paper will first survey the hyperincursive and incursive algorithms to discretize the classical harmonic oscillator. These algorithms show stable orbital with the conservation of energy.
D. Dubois
semanticscholar   +1 more source

Quantum-Mechanical Harmonic Oscillator

2018
Quantum-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.
openaire   +2 more sources

The quantum harmonic oscillator on a lattice

Journal of Physics A: Mathematical and General, 1986
The 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
openaire   +2 more sources

The quantum damped harmonic oscillator

Physics Reports, 2002
Abstract Starting with the quantization of the Caldirola–Kanai Hamiltonian, various phenomenological methods to treat the damped harmonic oscillator as a dissipative system are reviewed in detail. We show that the path integral method yields the exact quantum theory of the Caldirola–Kanai Hamiltonian without violation of Heisenberg's uncertainty ...
C. I. Um, Kyu-Hwang Yeon, Thomas F. George   +2 more
openaire   +2 more sources

A novel digital contents privacy scheme based on quantum harmonic oscillator and schrodinger paradox

Wirel. Networks, 2020
Abdullah A. Alghafis, H. Waseem, M. Khan, Sajjad Shaukat Jamal, Muhammad Amin, Syeda Iram Batool   +5 more
semanticscholar   +1 more source

Quantum Harmonic Oscillator and Schrodinger Paradox Based Nonlinear Confusion Component

International Journal of Theoretical Physics, 2020
Sundas Tariq, A. Elmoasry, Syeda Iram Batool, Majid Khan   +3 more
semanticscholar   +1 more source

Measuring the quantum harmonic oscillator

Frontiers in Optics 2010/Laser Science XXVI, 2010
By 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.
openaire   +2 more sources

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.
openaire   +1 more source

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.
openaire   +1 more source