SAIP2026

Solution of the two dimensional Schrödinger equation using Basis functions derived from the 16/8 Daubechies Wavelet Scaling Function

7 Jul 2026, 15:00

20m

Lecture Hall DL2 (University of the Western Cape)

Oral Presentation Track G - Theoretical and Computational Physics Theoretical and Computational Physics

Speaker

Moritz Braun (UNISA)

Description

We use two dimensional basis functions based on a shifted and scaled wavelet scaling sym8 function
\begin{equation}
f_i(x)=\phi\left( x/h+x_{\rm max} /h -i\right)/\sqrt{h}\,.
\end{equation}
Here $h=x_{\rm max}/N$, where $x_{\rm max}$ is the distance from the origin to he boundary of the square shaped domain. In addition we modify these functions to satisfy periodic boundary conditions to improve convergence, denoting these by $g_i(x)$. We make use of repeated Gauss Legendre integration on the grid.\
As test case we consider the two dimensional harmonic oscillator with the potential
$$ V(x,y)=x^2+y^2$$ It is found that the energies converge quite quickly to the analytical values. and examine the convergence as function of $N$.

Presentation materials

14_Moritz_Braun.pdf