Fundamentals of the Algebraic Version of the Resonating-Group Method in the One-Dimensional Case. I. Analytic Results
DOI:
https://doi.org/10.15407/ujpe70.7.425Keywords:
one-dimensional case, algebraic version of the resonating-group method, oscillator basis, matrix elements, asymptotics of coefficientsAbstract
The features of analytic calculations in the framework of the algebraic version of the resonatinggroup method, which is based on expanding the wave function of a quantum system on the basis of oscillator functions, have been examined in the one-dimensional case. The construction of the Hamiltonian matrix elements using the technique of generating functions and generating matrix elements has been discussed in detail. The asymptotic behavior is found for the coefficients in the wave function expansion in the oscillator function basis as the oscillator quantum number tends to infinity in the continuous spectrum case. The asymptotic dependence of the potential-energy matrix elements on the oscillator quantum number has been obtained for a Gaussian potential.
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