Formulation of Quantum Mechanics Based on the Quasi-Probability Distribution Induced on Phase Space

1958 ◽  
Vol 109 (6) ◽  
pp. 2198-2206 ◽  
Author(s):  
George A. Baker
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Probability Distribution

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.

Invariance Groups in Classical and Quantum Mechanics

1973 ◽  
Vol 28 (3-4) ◽  
pp. 538-540 ◽  
Author(s):  
D. J. Simms
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Energy Levels ◽  
Classical Mechanics ◽  
Symmetry Groups ◽  
Casimir Invariants ◽  
Classical Phase Space ◽  
Invariance Groups ◽  
Classical And Quantum Mechanics

AbstractThis is a report on some new relations and analogies between classical mechanics and quantum mechanics which arise out of the work of Kostant and Souriau. Topics treated are i) the role of symmetry groups; ii) the notion of elementary system and the role of Casimir invariants; iii) energy levels; iv) quantisation in terms of geometric data on the classical phase space. Some applications are described.

Quantum mechanics in phase space II.

1977 ◽  
Vol 87 (1) ◽  
pp. 132-144 ◽  
Author(s):  
J.G. Krüger ◽  
A. Poffyn
Keyword(s):  
Quantum Mechanics ◽  
Phase Space
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