Harmonic Oscillator in a 1D or 2D Cavity with General Perfectly Reflecting Walls

We investigate the simple harmonic oscillator in a 1-d box, and the 2-d isotropic harmonic oscillator problem in a circular cavity with perfectly reflecting boundary conditions. The energy spectrum has been calculated as a function of the self-adjoint extension parameter. For sufficiently negative values of the self-adjoint extension parameter, there are bound states localized at the wall of the box or the cavity that resonate with the standard bound states of the simple harmonic oscillator or the isotropic oscillator. A free particle in a circular cavity has been studied for the sake of comparison. This work represents an application of the recent generalization of the Heisenberg uncertainty relation related to the theory of self-adjoint extensions in a finite volume.

Root system of singular perturbations of the harmonic oscillator type operators

We analyze perturbations of the harmonic oscillator type operators in a Hilbert space H, i.e. of the self-adjoint operator with simple positive eigenvalues μ k satisfying μ k+1 − μ k ≥ Δ > 0. Perturbations are considered in the sense of quadratic forms. Under a local subordination assumption, the eigenvalues of the perturbed operator become eventually simple and the root system contains a Riesz basis.

Sideband characterization and atmospheric observations with various 340 GHz heterodyne receivers

This paper describes sideband response measurements and atmospheric observations with a double sideband and two Single Sideband (SSB) receiver prototypes developed for the multi-beam limb sounder instrument stratosphere-troposphere exchange and climate monitor radiometer. We first show an advanced Fourier-Transform Spectroscopy (FTS) method for sideband response and spurious signal characterization. We then present sideband response measurements of the different prototype receivers and we compare the results of the SSB receivers with sideband measurements by injecting a continuous wave signal into the upper and lower sidebands. The receivers were integrated into a total-power radiometer and atmospheric observations were carried out. The observed spectra were compared to forward model spectra to conclude on the sideband characteristics of the different receivers. The two sideband characterization methods show a high degree of agreement for both SSB receivers with various local oscillator settings. The measured sideband response was used to correct the forward model simulations. This improves the agreement with the atmospheric observations and explains spectral features caused by an unbalanced sideband response. The FTS method also allows to quantify the influence of spurious harmonic responses of the receiver.

Sideband-Ratio and Harmonic Response of Sub-Millimeter Wave Mixers measured with a Martin Puplett Interferometer

Heterodyne receivers at millimeter and submillimeter wavelength are widely used for radiometric spectral line observations for atmospheric remote sensing or radio astronomy. The quantitative analysis of such observations requires an accurate knowledge of the mixers's sideband ratio. In addition, its potential sensitivity to spurious harmonics needs to be well understood. In this paper, we discuss a measurement technique for these receiver characteristics, which is based on a scanning Martin Puplett Interferometer used in conjunction with a wide band digital autocorrelation spectrometer for the analysis of the intermediate frequency band. We present measurement results of different double sideband and sideband separating mixers, which were developed for the proposed 340GHz multi-beam limb sounder STEAMR.