Hello,(adsbygoogle = window.adsbygoogle || []).push({});

I would like to ask something about central potentials. When I am working in 3D, I haven´t got any problem solving the schrodinger equation since I use the following change of variables:

[tex]-\frac{\hbar^{2}}{2m}\nabla^{2}\Psi+V(r)\Psi=E\Psi[/tex]

[tex]\Psi=\frac{\chi}{r}[/tex]

With this change of variables, I can solve and understand the equation, but when I am working in 2D( usig r and [tex]\varphi[/tex]) I can't solve the equation because the laplacian is different. The concrete potential distribution I want to study is the following:

[tex]V(\vec{r})=0 \stackrel{if}{\rightarrow} r<a[/tex]

[tex]V(\vec{r})=\infty \stackrel{if}{\rightarrow} r>a[/tex]

And I would like to solve the equation for the first and the second energy levels of the system. I would appreciate some tips, thank you.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Schrodinger Equation for a central 2D potential

Loading...

Similar Threads - Schrodinger Equation central | Date |
---|---|

I Can the Schrodinger equation satisfy Laplace's equation? | Feb 22, 2018 |

I Hamiltonian in Schrödinger: necessarily total energy? | Feb 22, 2018 |

A What form of the Schrodinger equation do you use for intensity? | Feb 9, 2018 |

I Question about the solution to the Harmonic wave equation | Feb 3, 2018 |

I I am interested in Schrodinger equation with tempor. element | Feb 3, 2018 |

**Physics Forums - The Fusion of Science and Community**