The time-dependent Hartree-Fock equations are derived from the N -body linear Schrödinger equation with mean-field scaling in the limit N → ∞ and for initial data that are like Slater determinants. Only the case of bounded, symmetric interaction potentials is treated in this work. We prove that, as N → ∞, the first partial trace of the Nbody density operator approaches the solution of the time-dependent Hartree-Fock equations (in operator form) in the trace norm.

We propose to quantify the correlation inherent in a many-electron (or many-fermion) wave function psi by comparing it to the unique uncorrelated state that has the same 1-particle density operator as does /|psi>

PURPOSE To analyze the prevalence of SARS-CoV-2 infection in patients with cancer in hospital care after implementation of institutional and governmental safety measurements. METHODS Patients with cancer routinely tested for SARS-CoV-2 RNA by nasal swab and real-time polymerase chain reaction between March 21 and May 4, 2020, were included. The results of this cancer cohort were statistically compared with the SARS-CoV-2 prevalence in the Austrian population as determined by a representative nationwide random sample study (control cohort 1) and a cohort of patients without cancer presenting to our hospital (control cohort 2). RESULTS A total of 1,688 SARS-CoV-2 tests in 1,016 consecutive patients with cancer were performed. A total of 270 of 1,016 (26.6%) of the patients were undergoing active anticancer treatment in a neoadjuvant/adjuvant and 560 of 1,016 (55.1%) in a palliative setting. A total of 53 of 1,016 (5.2%) patients self-reported symptoms potentially associated with COVID-19. In 4 of 1,016 (0.4%) patients, SARS-CoV-2 was detected. At the time of testing at our department, all four SARS-CoV-2–positive patients were asymptomatic, and two of them had recovered from symptomatic COVID-19. Viral clearance was achieved in three of the four patients 14-56 days after testing positive. The estimated odds ratio of SARS-CoV-2 prevalence between the cancer cohort and control cohort 1 was 1.013 (95% CI, 0.209 to 4.272; P = 1), and between control cohort 2 and the cancer cohort it was 18.333 (95% CI, 6.056 to 74.157). CONCLUSION Our data indicate that continuation of active anticancer therapy and follow-up visits in a large tertiary care hospital are feasible and safe after implementation of strict population-wide and institutional safety measures during the current COVID-19 pandemic. Routine SARS-CoV-2 testing of patients with cancer seems advisable to detect asymptomatic virus carriers and avoid uncontrolled viral spread.