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Note on calculations by hypervirial relations and sufficient conditions for these relations: Box potential and harmonic oscillator models
Author(s) -
Terasaka Toshitaka,
Sakamoto Kazuyoshi
Publication year - 1982
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560210303
Subject(s) - harmonic oscillator , wave function , diagonal , harmonic , function (biology) , excitation , potential energy , energy (signal processing) , mathematics , quantum mechanics , physics , mathematical analysis , geometry , evolutionary biology , biology
The calculations by the diagonal and the off‐diagonal hypervirial relations and by the sufficient conditions for these relations have been performed for the one‐dimensional box potential and the harmonic oscillator models. In the case of the box potential model, the variation method gave the unsymmetrical wave functions for trial functions though it gave the best energies, but some of these hypervirial calculations gave the symmetrical functions and therefore they showed the exact expectation values of x , though they did not give the best energies. On the contrary, in the case of the harmonic oscillator model such a discrepancy for wave function and excitation energy did not happen. For the box potential model the expectation values of some operators were evaluated and compared with the results by the exact solution and the variation method. A weakness of the off‐diagonal hypervirial calculation was pointed out and the removal of this weakness was tried. The effectiveness of these calculations were investigated.