Custodian
发表于 2025-3-27 00:31:02
The Poisson Bracket and Symplectic Geometry,We have seen that the quantum theory of a free particle corresponds to the construction of a representation of the Heisenberg Lie algebra in terms of operators . and ., together with a choice of Hamiltonian ..
SSRIS
发表于 2025-3-27 01:10:10
Quadratic Polynomials and the Symplectic Group,In Chapters . and ., we studied in detail the Heisenberg Lie algebra as the Lie algebra of linear functions on phase space.
farewell
发表于 2025-3-27 09:06:29
Semi-direct Products,The theory of a free particle is largely determined by its group of symmetries, the group of symmetries of three-dimensional space, a group which includes a subgroup . of spatial translations, and a subgroup .(3) of rotations.
引起
发表于 2025-3-27 09:34:17
Peter WoitSystematically emphasizes the role of Lie groups, Lie algebras, and their unitary representation theory in the foundations of quantum mechanics.Introduces fundamental structures and concepts of repres
forecast
发表于 2025-3-27 16:32:29
http://reply.papertrans.cn/79/7816/781519/781519_35.png
Isthmus
发表于 2025-3-27 21:03:36
http://reply.papertrans.cn/79/7816/781519/781519_36.png
tooth-decay
发表于 2025-3-27 22:31:53
Momentum and the Free Particle, moving in physical space .. This is something quite different from the classical mechanical description of a free particle, which will be reviewed in chapter .. A common way of motivating this is to begin with the 1924 suggestion by de Broglie that just as photons may behave like either particles o
Debrief
发表于 2025-3-28 06:05:35
Hamiltonian Vector Fields and the Moment Map,n’s equations .and the tangent vectors of these parametrized curves provide a vector field on phase space. Such vector fields are called Hamiltonian vector fields. There is a distinguished choice of ., the Hamiltonian function ., which gives the velocity vector fields for time evolution trajectories
opprobrious
发表于 2025-3-28 10:06:41
http://reply.papertrans.cn/79/7816/781519/781519_39.png
Desert
发表于 2025-3-28 14:20:18
The Quantum Free Particle as a Representation of the Euclidean Group,known for relativistic theories, where it is the representation theory of the Poincaré group that is relevant, a topic that will be discussed in chapter .. It is less well known that even in the non-relativistic case, the Euclidean group .(3) of symmetries of space plays a similar role, with irreduc