Exact calculation of the trace of the Birman–Schwinger operator of the one-dimensional harmonic oscillator perturbed by an attractive Gaussian potential

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The behaviour of the three-dimensional Hamiltonian -Δ+λ[δ(x+x0)+δ(x-x0)] as the distance between the two centres vanishes

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Spectral properties of a symmetric three-dimensional quantum dot with a pair of identical attractive δ-impurities symmetrically situated around the origin II

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Spectral properties of a short-range impurity in a quantum dot

The spectral properties of the quantum mechanical system consisting of a quantum dot with a short-range attractive impurity inside the dot are investigated in the zero-range limit. The Green function of the system is obtained in an explicit form. In the case of a spherically symmetric quantum dot, the dependence of the spectrum on the impurity position and the strength of the impurity potential is analyzed in detail. It is proven that the confinement potential of the dot can be recovered from the spectroscopy data. The consequences of the hidden symmetry breaking by the impurity are considered. The effect of the positional disorder is studied.Comment: 30 pages, 6 figures, Late

A Note on the Discrete Spectrum of Gaussian Wells (I): The Ground State Energy in One Dimension

The ground state energy is computed for small values of by means of an approximation of an integral operator in momentum space. Such an approximation leads to a transcendental equation for which 0 ( ) = | 0 ( )

Surgical resection is superior to TACE in the treatment of HCC in a well selected cohort of BCLC-B elderly patients—A retrospective observational study

Simple Summary Hepatocellular carcinoma (HCC) is the most common primary liver malignancy. Liver transplantation (LT) and surgical resection (SR) are currently the primary treatments with curative intent. Nevertheless, more than two-thirds of patients are elderly and, therefore, excluded from LT; while, according to the Barcelona Clinic Liver Cancer (BCLC) system, SR should only be offered to a small group of patients with early stage HCC. The identification in stage B of an intermediate subgroup of patients that fulfill the criteria for surgery may play an important role in the implementation of potentially curative treatments. Hepatocellular carcinoma (HCC) usually develops in cirrhotic liver, with high recurrence rates. However, considering its increasing detection in non-cirrhotic liver, the choice of treatment assumes particular relevance. This study aimed to investigate outcomes of patients among BCLC stages and enrolled for surgical resection (SR) according to a more complex evaluation, to establish its safety and efficacy. A total of 186 selected HCC patients (median age 73.2 yrs), submitted to SR between January 2005 and January 2021, were retrospectively analyzed. Of which, 166 were staged 0, A, B according to the BCLC system, while 20 with a single large tumor (>5 cm) were classified as stage AB. No perioperative mortality was recorded; complications occurred in 48 (25.80%) patients, and all but two were Clavien-Dindo grade I-II. Median follow-up was 9.2 years. Subsequently, 162 recurrent patients (87,1%) were selected for new treatments. Comparable overall survival rates (OS) were observed at 1, 3, 5, and 10 years in 0, A, B and AB stages (p = 0.2). Eventually, the BCLC-B group was matched to 40 BCLC-B patients treated (2015-2021) with TACE. Significant differences in baseline characteristics (p <0.0001) and in OS were observed at 1 and 3 years (p <0.0001); a significant difference was also observed in oncological outcomes, in terms of the absence, residual, or relapse of disease (p <0.05). Surgery might be a valid treatment in HCC for patients affected by chronic liver disease in a condition of compensation, up to BCLC-B stage. Surgical indication for liver resection in case of HCC should be extensively revised