Quantum dynamics
In physics, quantum dynamics is the quantum version of
In mathematics, quantum dynamics is the study of the mathematics behind
Relation to classical dynamics
Equations to describe quantum systems can be seen as equivalent to that of classical dynamics on a macroscopic scale, except for the important detail that the variables don't follow the commutative laws of multiplication.[5] Hence, as a fundamental principle, these variables are instead described as "q-numbers", conventionally represented by operators or Hermitian matrices on a Hilbert space.[6] Indeed, the state of the system in the atomic and subatomic scale is described not by dynamic variables with specific numerical values, but by state functions that are dependent on the c-number time. In this realm of quantum systems, the equation of motion governing dynamics heavily relies on the Hamiltonian, also known as the total energy. Therefore, to anticipate the time evolution of the system, one only needs to determine the initial condition of the state function |Ψ(t) and its first derivative with respect to time.[7]
For example, quasi-free states and automorphisms are the Fermionic counterparts of classical Gaussian measures[8] (Fermions' descriptors are Grassmann operators).[6]
See also
- Quantum Field Theory
- Perturbation theory
- Semigroups
- Pseudodifferential operators
- Brownian motion
- Dilation theory
- Quantum probability
- Free probability
References
- ^ Joan Vaccaro (2008-06-26). "Centre for Quantum Dynamics, Griffith University". Quantiki. Archived from the original on 2009-10-25. Retrieved 2010-01-25.
- ^
ISBN 9780387229645.
- ^
Teufel, Stefan (1821-01-01). Adiabatic perturbation theory in quantum dynamics. Springer. ISBN 9783540407232.
- OCLC 52901091.
- ISSN 0950-1207.
- ^ PMID 35909420.
- ISBN 978-0-521-82952-6.
- ISBN 978-0-19-850400-9.
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