On the relation between Schrödinger and von Neumann equations

Man'ko, V. I. ; Marmo, G. ; Sudarshan, E. C. G. ; Zaccaria, F. (1999) On the relation between Schrödinger and von Neumann equations Journal of Russian Laser Research, 20 (5). pp. 421-437. ISSN 1071-2836

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Official URL: http://www.springerlink.com/content/m2272017421u3g...

Related URL: http://dx.doi.org/10.1007/BF02508909


The relation between the density matrix obeying the von Neumann equation and the wave function obeying the Schrödinger equation is discussed in connection with the superposition principle of quantum states. The definition of the ray-addition law is given, and its relation to the addition law of vectors in the Hilbert space of states and the role of a constant phase factor of the wave function is elucidated. The superposition law of density matrices, Wigner functions, and tomographic probabilities describing quantum states in the probability representation of quantum mechanics is studied. Examples of spin-½ and Schrödinger-cat states of the harmonic oscillator are discussed. The connection of the addition law with the entanglement problem is considered.

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ID Code:50927
Deposited On:27 Jul 2011 13:00
Last Modified:18 May 2016 05:03

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