Timeline for Extending a solution for $\left(H_\text{osc} + \delta^{(3)}(\vec r) \frac{\partial}{\partial r} r \right) \Psi(\vec r)$ to Gaussian potentials
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 16, 2014 at 18:47 | vote | accept | Martin Ueding | ||
| Apr 30, 2014 at 9:08 | comment | added | Martin Ueding | The problem I have to solve is a one-particle-problem. It is a single anharmonic oscillator. Therefore, separability is not a problem. I think I only need the relative part anyway, since that is a one particle problem. | |
| Apr 29, 2014 at 21:36 | comment | added | DumpsterDoofus | There's one issue that will have to be considered: in the paper, the fact that the trap potential is harmonic is essential to the separability of $H=H_\text{CM}+H_\text{rel}$, which relies on the identity $\mathbf{r}_1^2+\mathbf{r}_2^2=\mathbf{R}^2+\mathbf{r}^2$ where $\mathbf{R}=2^{-1/2}(\mathbf{r}_1+\mathbf{r_2})$ and $\mathbf{r}=2^{-1/2}(\mathbf{r}_1-\mathbf{r_2})$. Because of this, the eigenstates become tensor-products of the eigenstates of $H_\text{CM}$ and $H_\text{rel}$. If you want to modify it to use an anharmonic trap, this separability is probably going to be spoiled. | |
| Apr 29, 2014 at 18:31 | answer | added | Brian Moths | timeline score: 2 | |
| Apr 29, 2014 at 17:14 | history | edited | Martin Ueding | CC BY-SA 3.0 |
edited title
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| Apr 29, 2014 at 17:03 | history | edited | Danu | CC BY-SA 3.0 |
deleted 1 character in body
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| Apr 29, 2014 at 16:58 | history | asked | Martin Ueding | CC BY-SA 3.0 |