5
votes
2answers
123 views

Eigenvalue problem for differential equations in QM

I have a very simple question with regard to numerical methods in physics. I want to solve the eigenvalue problem for a particle moving in an arbitrary potential. Let's take 1D to be concrete. I.e. I ...
4
votes
2answers
793 views

Radial Schrodinger equation with inverse power law potential

Recently I read a paper about solving radial Schrodinger equation with inverse power law potential. Consider the radial Schrodinger equation(simply set $\mu=\hbar=1$): ...
7
votes
2answers
3k views

Solving one dimensional Schrodinger equation with finite difference method

Consider the one-dimensional Schrodinger equation $$-\frac{1}{2}D^2 \psi(x)+V(x)\psi(x)=E\psi(x)$$ where $D^2=\dfrac{d^2}{dx^2},V(x)=-\dfrac{1}{|x|}$. I want to calculate the ground state ...
4
votes
2answers
998 views

On numerically solving the Schrödinger equation

I just read a paper 'A pocket calculator determination of energy eigenvalues' by J Killingbeck (1979). Link: http://iopscience.iop.org/0305-4470/10/6/001 I have some questions about section 2. Why ...