Reply to the Comment on ``On the uncertainty relations and squeezed states for the quantum mechanics on a circle''

On the uncertainty relations and squeezed states for the quantum mechanics on a circle

The uncertainty relations for the position and momentum of a quantum particle on a circle are identified minimized by the corresponding coherent states. The sqeezed states in the case of the circular motion are introduced and discussed in the context of the uncertainty relations.

Comment on "On the uncertainty relations and squeezed states for the quantum mechanics on a circle"

It is shown by examples that the position uncertainty on a circle, proposed recently by Kowalski and Rembieliński [J. Phys. A 35 (2002) 1405] is not consistent with the state localization. We argue that the relevant uncertainties and uncertainty relations (UR's) on a circle are that based on the Gram-Robertson matrix. Several of these generalized UR's are displayed and related criterions for squeezed states are discussed.

对《广义压缩态的性质和动力学》的回复

Reply to Comment on "Properties and dynamics of generalized squeezed states"

本文回应了关于广义压缩态振荡动力学的评论，指出其物理定义问题，并通过附加信息明确定义，同时反驳了光子数单调增加的主张。

Completeness of photon-added squeezed vacuum and one-photon-states and of photon-added coherent states on a circle

A discrete completeness relation and a continuous one with a positive measure are found for the photon-added squeezed vacuum states. Extension to the photon-added squeezed one-photon states is considered. Photon-added coherent states on a circle are introduced. Their normalization and unity resolution relation are given.

Squeezed States of a Particle in Magnetic Field

For a charged particle in a homogeneous magnetic field, we construct stationary squeezed states which are eigenfunctions of the Hamiltonian and the non-Hermitian operator $\hat{X}_Φ = \hat{X} \cos Φ+ \hat{Y} \sin Φ$, $\hat{X}$ and $\hat{Y}$ being the coordinates of the Larmor circle center and $Φ$ is a complex parameter. In the family of the squeezed states, the quantum uncertainty in the Larmor circle position is minimal. The wave functions of the squeezed states in the coordinate representation are found and their properties are discussed. Also, for arbitrary gauge of the vector potential we…

Localization properties of squeezed quantum states in nanoscale space domains

We construct families of squeezed quantum states on an interval (depending on boundary conditions, we interpret the interval as a circle or as the infinite square potential well) and obtain estimates of position and momentum dispersions for these states. A particular attention is paid to the possibility of proper localization of a particle in nanoscale space domains. One of the constructed family of squeezed states is based on the theta function. It is a generalization of the known coherent and squeezed states on the circle. Also we construct a family of squeezed states based on truncated Gaus…