Euclidean quantum mechanics and stochastic integrals

1981 ◽  
pp. 371-393 ◽  
Author(s):  
R. F. Streater
Keyword(s):  
Quantum Mechanics ◽  
Stochastic Integrals

scholarly journals A Feynman–Kac formula for magnetic monopoles

2021 ◽  
pp. 2150015
Author(s):  
J. Dimock
Keyword(s):  
Quantum Mechanics ◽  
Charged Particle ◽  
Line Bundle ◽  
Eigenfunction Expansion ◽  
Magnetic Monopole ◽  
Magnetic Monopoles ◽  
Wave Functions ◽  
Stochastic Integrals ◽  
Complex Line ◽  
Imaginary Time

We consider the quantum mechanics of a charged particle in the presence of Dirac’s magnetic monopole. Wave functions are sections of a complex line bundle and the magnetic potential is a connection on the bundle. We use a continuum eigenfunction expansion to find an invariant domain of essential self-adjointness for the Hamiltonian. This leads to a proof of the Feynman–Kac formula expressing solutions of the imaginary time Schrödinger equation as stochastic integrals.

Quantum Mechanics

2009 ◽  
Author(s):  
Gennaro Auletta ◽  
Mauro Fortunato ◽  
Giorgio Parisi
Keyword(s):  
Quantum Mechanics

Quantum Mechanics for Nanostructures

2009 ◽  
Author(s):  
Vladimir V. Mitin ◽  
Dmitry I. Sementsov ◽  
Nizami Z. Vagidov
Keyword(s):  
Quantum Mechanics

The Logic of Quantum Mechanics

1984 ◽  
Author(s):  
Enrico G. Beltrametti ◽  
Gianni Cassinelli ◽  
Peter A. Carruthers
Keyword(s):  
Quantum Mechanics
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