Expectation Values of Singular Operators in Variational Calculations of Atomic P-States
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Date
2020-05-05
Authors
Shomenov, Toreniyaz
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Publisher
Nazarbayev University School of Sciences and Humanities
Abstract
Expectation values of singular operators evaluated in the framework of the Rayleigh-Ritz
variational method in quantum mechanics may show slow convergence with increasing
the number of basis functions, K. An example of such commonly used operator in the
case of high-accuracy calculations of few-electron atoms and molecules is the Dirac delta
function dependent on interparticle distances, δ(rij). One way to improve the convergence
is to adopt the expectation value identities, in which the singular operator is replaced by
an certain non-singular operator so that the expectation value is the same in the limit
when the trial wave function approaches the exact solution to the Schrödinger equation.
However, when the wave function is approximate, which takes place for any finite K, the
convergence of the expectation value of this equivalent non-singular operator is usually
improved, often by orders of magnitude. In this thesis, we provide the derivation of
formulas for such expectation value identities and implement them into a computer code
for the case of atomic P-states, whose wave function is expanded in terms of all-particle
explicitly correlated Gaussian basis functions.
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Citation
Shomenov, T. (2020).Expectation Values of Singular Operators in Variational Calculations of Atomic P-States (Master’s thesis, Nazarbayev University, Nur-Sultan, Kazakhstan). Retrieved from https://nur.nu.edu.kz/handle/