scholarly journals Convexity and the separability problem of quantum mechanical density matrices

2002 ◽  
Vol 346 (1-3) ◽  
pp. 47-71 ◽  
Author(s):  
Arthur O. Pittenger ◽  
Morton H. Rubin
Keyword(s):  
Quantum Mechanical ◽  
Density Matrices ◽  
Separability Problem

On the error of approximations in quantum mechanics. I. General theory

1965 ◽  
Vol 257 (1081) ◽  
pp. 309-326 ◽  
Keyword(s):  
Quantum Mechanics ◽  
General Theory ◽  
Computer Applications ◽  
Quantum Mechanical ◽  
Quantum Mechanical Calculations ◽  
Density Matrices ◽  
Single Error

General formulas for estimating the errors in quantum-mechanical calculations are given in the formalism of density matrices. Some properties of the traces of matrices are used to simplify the estimating and to indicate a way of obtaining a better approximation. It is shown that the simultaneous correction of all the equations to be fulfilled leads in most cases to a faster convergence than the exact fulfilment of some of the equations and approximating stepwise to some of the others. The corrective formulas contain only direct operations of the matrices occurring and so they are advantageous in computer applications. In the last section a ‘subjective error’ definition is given and by taking into account the weight of the errors of the several equations a faster convergence and a single error quantity is obtained. Some special applications of the method will be published later.

Phase Space, Density Matrices, Energy Densities, and Exchange Holes

2001 ◽  
Vol 215 (10) ◽  
Author(s):  
M. Springborg ◽  
J. P. Perdew ◽  
K. Schmidt
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Momentum Space ◽  
Classical Mechanics ◽  
Quantum Mechanical ◽  
Phase Space Density ◽  
Density Matrices ◽  
Space Density

In the general case, quantum-mechanical quantities are represented by operators in position- or momentum-space representations, but in phase space they are represented by functions. The correspondence between classical mechanics and quantum mechanics is non-unique as a consequence of [

5.—Mott Scattering and Stern-Gerlach Effect

1972 ◽  
Vol 71 (1) ◽  
pp. 51-59
Author(s):  
P. S. Farago
Keyword(s):  
Point Of View ◽  
Quantum Mechanical ◽  
Density Matrices ◽  
Standard Quantum ◽  
Type Experiment ◽  
Mechanical Formalism ◽  
Quantum Mechanical Formalism ◽  
Stokes Vectors ◽  
Mott Scattering

SynopsisIt is shown that, from an operational point of view, the production and detection of spin-polarised electrons by Mott scattering is equivalent to the performance of a Stern-Gerlach type experiment with heavy spin-one-half particles. The argument is based on standard quantum mechanical formalism using density matrices and Stokes vectors for the description of polarised assemblies of particles.

scholarly journals Quantum Harmonic Analysis of the Density Matrix

Quanta ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 74 ◽  
Author(s):  
Maurice A. De Gosson
Keyword(s):  
Density Matrix ◽  
Harmonic Analysis ◽  
Quantum Mechanical ◽  
Mixed States ◽  
Density Matrices ◽  
Planck’S Constant ◽  
Planck's Constant

We will study rigorously the notion of mixed states and their density matrices. We will also discuss the quantum-mechanical consequences of possible variations of Planck's constant h. This review has been written having in mind two readerships: mathematical physicists and quantum physicists. The mathematical rigor is maximal, but the language and notation we use throughout should be familiar to physicists.Quanta 2018; 7: 74–110.

On ``Diagonal'' Coherent‐State Representations for Quantum‐Mechanical Density Matrices

1965 ◽  
Vol 6 (5) ◽  
pp. 734-739 ◽  
Author(s):  
John R. Klauder ◽  
James McKenna ◽  
Douglas G. Currie
Keyword(s):  
Coherent State ◽  
Quantum Mechanical ◽  
Density Matrices

Operators and meaning of wave function

2016 ◽  
pp. 4039-4042
Author(s):  
Viliam Malcher
Keyword(s):  
Wave Function ◽  
Quantum Theory ◽  
State Vector ◽  
The State ◽  
Physical Significance ◽  
Central Problem ◽  
Quantum Mechanical ◽  
Mechanical Description ◽  
Quantum Mechanical Description ◽  
Interpretation Of Quantum Theory

The interpretation problems of quantum theory are considered. In the formalism of quantum theory the possible states of a system are described by a state vector. The state vector, which will be represented as |ψ> in Dirac notation, is the most general form of the quantum mechanical description. The central problem of the interpretation of quantum theory is to explain the physical significance of the |ψ>. In this paper we have shown that one of the best way to make of interpretation of wave function is to take the wave function as an operator.

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