EVALUATION OF FUNCTIONAL INTEGRALS GENERATED BY SOME NONRELATIVISTIC HAMILTONIANS
https://doi.org/10.29235/1561-2430-2018-54-1-44-49
Abstract
The numerical results for functional integrals with respect to the conditional Wiener measure, generated by the Hamiltonian of a harmonic oscillator, the Hamiltonian of an anharmonic oscillator and the Hamiltonian of a one-dimensional rectangular well, are obtained in the work. Numerical results are obtained using the method based on the expansion in eigenfunctions of the Hamiltonian generating a functional integral. Evaluation of eigenvalues used in the expansion is based on counting the number of matches of signs of terms of the Sturm sequence. Therefore this method is stable to the accumulation of errors and is well implemented on a computer. The proposed method is more effective than the previously known methods for evaluation of functional integrals over the space of functions given on long intervals.
About the Author
V. B. Malyutin
Institute of Mathematics of the National Academy of Sciences of Belarus, Minsk
Belarus
Ph. D. (Physics and Mathematics), Leading Researcher
Belarus
Ph. D. (Physics and Mathematics), Leading Researcher
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