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1 - Introduction
Jerome R. Busemeyer, Indiana University, Peter D. Bruza, Queensland University of Technology
Book:

Quantum Models of Cognition and Decision

Published online:

14 November 2024

Print publication:

21 November 2024, pp 1-20
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6 - Introductory Dynamics
Jerome R. Busemeyer, Indiana University, Peter D. Bruza, Queensland University of Technology
Book:

Quantum Models of Cognition and Decision

Published online:

14 November 2024

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21 November 2024, pp 178-209
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Principles and Applications
2nd edition
Jerome R. Busemeyer, Peter D. Bruza
Published online:

14 November 2024

Print publication:

21 November 2024
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Quantum Models of Cognition and Decision, Second Edition presents a fully updated and expanded version of this innovative and path-breaking text. It offers an accessible introduction to the intersection of quantum theory and cognitive science, covering new insights, modelling techniques, and applications for understanding human cognition and decision making. In it, Busemeyer and Bruza delve into such topics as the non-commutative nature of judgments, quantum interference as a general principle governing human decision making, contextuality in modelling human cognition, and thought-provoking speculation about what a quantum approach to cognition might reveal about the ultimate nature of the human mind. Additions include new material on measurement, open systems, and applications to computer science. Requiring no prior background in quantum physics, this book comes complete with a tutorial and fully worked-out applications in important areas of cognition and decision.

14 - Transition Rules
from Part III - A Short Course in Quantum Field Theory
David W. Snoke, University of Pittsburgh
Book:

Interpreting Quantum Mechanics

Published online:

09 May 2024

Print publication:

16 May 2024, pp 201-218
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Summary

This chapter surveys several different mathematical methods for time-dependent change of quantum states using quantum field theory. The Bloch sphere method is introduced, which can be used to show the physics discussed in Chapter 3, that electronic transitions, or “jumps,” are not instantaneous.

Numerical Path Integral Approach to Quantum Dynamics and Stationary Quantum States
Part of
- Quantum theory
- Integral equations, integral transforms
Ilkka Ruokosenmäki, Tapio T. Rantala
Journal:

Communications in Computational Physics / Volume 18 / Issue 1 / July 2015

Published online by Cambridge University Press:

03 July 2015, pp. 91-103

Print publication:

July 2015
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Applicability of Feynman path integral approach to numerical simulations of quantum dynamics of an electron in real time domain is examined. Coherent quantum dynamics is demonstrated with one dimensional test cases (quantum dot models) and performance of the Trotter kernel as compared with the exact kernels is tested. Also, a novel approach for finding the ground state and other stationary sates is presented. This is based on the incoherent propagation in real time. For both approaches the Monte Carlo grid and sampling are tested and compared with regular grids and sampling. We asses the numerical prerequisites for all of the above.

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