Classical limit of the path‐integral formulation of quantum mechanics in terms of the density matrix

1987 ◽  
Vol 55 (2) ◽  
pp. 159-163 ◽  
Author(s):  
Pimon Ajanapon
Keyword(s):  
Quantum Mechanics ◽  
Density Matrix ◽  
Path Integral ◽  
Classical Limit ◽  
Integral Formulation ◽  
Path Integral Formulation

scholarly journals Path Integrals, Spontaneous Localisation, and the Classical Limit

2020 ◽  
Vol 75 (2) ◽  
pp. 131-141 ◽  
Author(s):  
Bhavya Bhatt ◽  
Manish Ram Chander ◽  
Raj Patil ◽  
Ruchira Mishra ◽  
Shlok Nahar ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Density Matrix ◽  
Path Integral ◽  
Classical Limit ◽  
Measurement Problem ◽  
Path Integrals ◽  
Path Integral Formulation ◽  
Von Neumann ◽  
Matrix Evolution ◽  
Grw Model

AbstractThe measurement problem and the absence of macroscopic superposition are two foundational problems of quantum mechanics today. One possible solution is to consider the Ghirardi–Rimini–Weber (GRW) model of spontaneous localisation. Here, we describe how spontaneous localisation modifies the path integral formulation of density matrix evolution in quantum mechanics. We provide two new pedagogical derivations of the GRW propagator. We then show how the von Neumann equation and the Liouville equation for the density matrix arise in the quantum and classical limit, respectively, from the GRW path integral.

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