scholarly journals CLASSICAL AND QUANTUM FREE MOTIONS IN THE TOMOGRAPHIC PROBABILITY REPRESENTATION

2012 ◽  
Vol 09 (02) ◽  
pp. 1260015
Author(s):  
V. I. MAN'KO ◽  
F. VENTRIGLIA
Keyword(s):  
Free Particle ◽  
Quantum States ◽  
Wave Functions ◽  
Probability Representation ◽  
Tomographic Probability ◽  
Density Operators ◽  
Tomographic Probability Representation ◽  
The Difference ◽  
Quantum Equations ◽  
Geometric Picture

Based on a geometric picture, the example of free particle motion for both classical and quantum domains is considered in the tomographic probability representation. Wave functions and density operators as well as optical and symplectic tomograms are obtained as solutions of kinetic classical and quantum equations for the state tomograms. The difference of tomograms of free particle for classical and quantum states is discussed.

scholarly journals Superposition Principle and Born’s Rule in the Probability Representation of Quantum States

2019 ◽  
Vol 1 (2) ◽  
pp. 130-150 ◽  
Author(s):  
Igor Ya. Doskoch ◽  
Margarita A. Man’ko
Keyword(s):  
Quantum Mechanics ◽  
Probability Distribution ◽  
Particle System ◽  
Superposition Principle ◽  
Quantum States ◽  
Particle State ◽  
Probability Representation ◽  
Tomographic Probability ◽  
Born’S Rule ◽  
System States

The basic notion of physical system states is different in classical statistical mechanics and in quantum mechanics. In classical mechanics, the particle system state is determined by its position and momentum; in the case of fluctuations, due to the motion in environment, it is determined by the probability density in the particle phase space. In quantum mechanics, the particle state is determined either by the wave function (state vector in the Hilbert space) or by the density operator. Recently, the tomographic-probability representation of quantum states was proposed, where the quantum system states were identified with fair probability distributions (tomograms). In view of the probability-distribution formalism of quantum mechanics, we formulate the superposition principle of wave functions as interference of qubit states expressed in terms of the nonlinear addition rule for the probabilities identified with the states. Additionally, we formulate the probability given by Born’s rule in terms of symplectic tomographic probability distribution determining the photon states.

scholarly journals MuSR method and tomographic-probability representation of spin states

2010 ◽  
Vol 31 (5) ◽  
pp. 421-442 ◽  
Author(s):  
Yury M. Belousov ◽  
Sergey N. Filippov ◽  
Vladimir N. Gorelkin ◽  
Vladimir I. Man’ko
Keyword(s):  
Spin States ◽  
Probability Representation ◽  
Tomographic Probability ◽  
Tomographic Probability Representation

Interference of Quantum States and Superposition Principle in Probability Representation of Quantum Mechanics

2019 ◽  
Vol 26 (03) ◽  
pp. 1950016 ◽  
Author(s):  
Margarita A. Man’ko ◽  
Vladimir I. Man’ko
Keyword(s):  
Quantum Mechanics ◽  
Probability Distributions ◽  
Superposition Principle ◽  
State Density ◽  
Quantum States ◽  
Density Matrices ◽  
Probability Representation ◽  
Density Operators ◽  
Pure States

The superposition of pure quantum states explicitly expressed in terms of a nonlinear addition rule of state density operators is reviewed. The probability representation of density matrices of qudit states is used to formulate the interference of the states as a combination of the probability distributions describing pure states. The formalism of quantizer–dequantizer operators is developed. Examples of spin-1/2 states and f-oscillator systems are considered.

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