23 Coherent States and the Propagator for the Harmonic Oscillator
In chapter 22 we found the energy eigenstates for the harmonic oscillator using annihilation and creation operator methods, and showed that these give a new construction of the representation of the Heisenberg group on the quantum mechanical state space, called the Bargmann-Fock representation. This representation comes with a distinguished state, the state |0⟩, and the Heisenberg group action takes this state to a set of states known as “coherent states”. These states are labeled by points of the phase space and provide the closest analog possible in the quantum system of classical states (i.e., those with a well-defined value of position and momentum variables).
Coherent states also evolve in time very simply, with their time evolution given just by the classical time evolution of the corresponding point in phase space. This fact can be used to calculate relatively straightforwardly the harmonic oscillator position space propagator, which gives the kernel for the action of time evolution on position space wavefunctions.
Chapter contents
- 23.1 Coherent states and the Heisenberg group action
- 23.2 Coherent states and the Bargmann-Fock state space
- 23.3 The Heisenberg group action on operators
- 23.4 The harmonic oscillator propagator
- 23.5 The Bargmann transform
- 23.6 For further reading
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正文：英文 · OCR 机器稿 · 待校对
核对状态：OCR 机器稿 · 待校对
原书 PDF · 印刷页 254、255、256、257、258、259、260、261、262、263、264、265
来源版本：2025-10-20
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