scholarly journals Generalized harmonic oscillators in quantum probability

1991 ◽  
pp. 39-51
Author(s):  
B. V. Rajarama Bhat ◽  
K. R. Parthasarathy
Keyword(s):  
Quantum Probability ◽  
Harmonic Oscillators ◽  
Generalized Harmonic Oscillators

scholarly journals Testing Quantum Coherence in Stochastic Electrodynamics with Squeezed Schrödinger Cat States

Atoms ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 42 ◽  
Author(s):  
Wayne Huang ◽  
Herman Batelaan
Keyword(s):  
Quantum Mechanics ◽  
Probability Distribution ◽  
Interference Pattern ◽  
Quantum Coherence ◽  
Laser Pulses ◽  
Quantum Probability ◽  
Harmonic Oscillators ◽  
Stochastic Electrodynamics ◽  
Schrödinger Cat ◽  
Cat States

The interference pattern in electron double-slit diffraction is a hallmark of quantum mechanics. A long-standing question for stochastic electrodynamics (SED) is whether or not it is capable of reproducing such effects, as interference is a manifestation of quantum coherence. In this study, we used excited harmonic oscillators to directly test this quantum feature in SED. We used two counter-propagating dichromatic laser pulses to promote a ground-state harmonic oscillator to a squeezed Schrödinger cat state. Upon recombination of the two well-separated wavepackets, an interference pattern emerges in the quantum probability distribution but is absent in the SED probability distribution. We thus give a counterexample that rejects SED as a valid alternative to quantum mechanics.

Generalized Harmonic Oscillators: Velocity Dependent Frequencies

2001 ◽  
Author(s):  
Ronald E. Mickens
Keyword(s):  
Nonlinear Oscillator ◽  
First Integral ◽  
Harmonic Oscillators ◽  
System Of Equations ◽  
Research Grants ◽  
Physical Systems ◽  
New Class ◽  
Generalized Harmonic Oscillators ◽  
Special Cases ◽  
Oscillator Equations

Abstract Preliminary results are given on a new class of nonlinear oscillator equations that generalize those of the usual linear harmonic case. These equations take the form ẋ = f(x)y and ẏ = −g(y)x, where f(x) and g(y) are continuous with first derivatives, and f(0) > 0, g(0) > 0. Of interest is the fact that these equations have a first-integral, i.e., there exists a function H(x,y) such that along a particular trajectory in the (x,y) phase space, H(x,y) = constant. We work out several general results related to this system of equations and illustrate them with several special cases that correspond to models of physical systems. The work reported here was supported in part by research grants from DOE and the MBRS-SCORE Program at Clark Atlanta University.

scholarly journals Exact wave functions for generalized harmonic oscillators

2011 ◽  
Vol 32 (4) ◽  
pp. 352-361 ◽  
Author(s):  
Nathan Lanfear ◽  
Raquel M. López ◽  
Sergei K. Suslov
Keyword(s):  
Wave Functions ◽  
Harmonic Oscillators ◽  
Generalized Harmonic Oscillators
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