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Quantization of the one-dimensional free harmonic oscillator as an example of the application of the node theorem and the MacDonald-Hylleraas-Undheim theorem
Kunle Adegoke, Adenike Olatinwo
Using heuristic arguments alone, based on the properties of the wavefunctions, we obtain the energy eigenvalues and the corresponding eigenfunctions of the one-dimensional harmonic…
An alternative derivation of the Fernández-Castro analytic approximate expression for the eigenvalues of the bounded quartic oscillator
Kunle Adegoke, Adenike Olatinwo, Gbenga Olunloyo
In this note we show that the standard \mbox{Rayleigh-Schrödinger} (RS) perturbation method gives the same result as the hypervirial pertubative method (HPM), for an approximate an…
On approximating the free harmonic oscillator by a particle in a box
Kunle Adegoke, Adenike Olatinwo, Henry Otobrise +2
The main purpose of this paper is to demonstrate and illustrate, once again, the potency of the variational technique as an approximation procedure for the quantization of quantum…
Exact diagonalization of the dimensional confined quantum harmonic oscillator
Kunle Adegoke, Adenike Olatinwo, Henry Otobrise +2
In the existing literature various numerical techniques have been developed to quantize the confined harmonic oscillator in higher dimensions. In obtaining the energy eigenvalues,…