Numerical methods for solving some singular boundary value problems of quantum mechanics and quantum field theory. I

1976 ◽  
Vol 22 (2) ◽  
pp. 150-170 ◽  
Author(s):  
A.T Filippov ◽  
I.V Puzynin ◽  
Dmitrij P Mavlo
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Numerical Methods ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Singular Boundary ◽  
Quantum Field ◽  
Singular Boundary Value Problems

Numerical methods for singular boundary value problems involving the p-laplacian

2009 ◽  
Author(s):  
Pedro Lima ◽  
Luisa Morgado ◽  
Alberto Cabada ◽  
Eduardo Liz ◽  
Juan J. Nieto
Keyword(s):  
Numerical Methods ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Singular Boundary ◽  
Singular Boundary Value Problems

Quantum mechanics

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Transition Amplitude ◽  
External Source ◽  
Quantum Field ◽  
Damping Term ◽  
Relativistic Quantum Theory ◽  
Generating Functional

After a brief review of the operator approach to quantum mechanics, Feynmans path integral, which expresses a transition amplitude as a sum over all paths, is derived. Adding a linear coupling to an external source J and a damping term to the Lagrangian, the ground-state persistence amplitude is obtained. This quantity serves as the generating functional Z[J] for n-point Green functions which are the main target when studying quantum field theory. Then the harmonic oscillator as an example for a one-dimensional quantum field theory is discussed and the reason why a relativistic quantum theory should be based on quantum fields is explained.

QLB for Quantum Many-Body and Quantum Field Theory

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Quantum Computing ◽  
Single Particle ◽  
Body Problem ◽  
Three Dimensions ◽  
Quantum Field ◽  
Many Body ◽  
Quantum Particles

Chapter 32 expounded the basic theory of quantum LB for the case of relativistic and non-relativistic wavefunctions, namely single-particle quantum mechanics. This chapter goes on to cover extensions of the quantum LB formalism to the overly challenging arena of quantum many-body problems and quantum field theory, along with an appraisal of prospective quantum computing implementations. Solving the single particle Schrodinger, or Dirac, equation in three dimensions is a computationally demanding task. This task, however, pales in front of the ordeal of solving the Schrodinger equation for the quantum many-body problem, namely a collection of many quantum particles, typically nuclei and electrons in a given atom or molecule.

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