Timeline for Where the time-dependent wavefunction $\Psi(\vec{x},t)$ lies?
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Feb 15, 2016 at 19:04 | comment | added | Emmanuel Boldrin | Thank you, guys! Could you point me some references/books, for a deeper study? | |
| Feb 15, 2016 at 16:45 | comment | added | yuggib | To complement, the usual smoothness requirement (in time) assumed for a solution $\psi(x,t)$ of the Schrödinger equation is continuity; therefore $\psi(\cdot)\in C^0(\mathbb{R},L^2(\mathbb{R}^3))$. The Schrödinger flow $\mathbf{S}\in C^0(\mathbb{R}\times L^2(\mathbb{R}^3), L^2(\mathbb{R}^3))\cap C^1(\mathbb{R}\times D(H), L^2(\mathbb{R}^3))$ is instead the map that associates to an initial datum $\psi_0\in L^2$ the solution $\mathbf{S}(t,\psi_0)$ of the Schrödinger equation at time $t$, and has the continuity properties mentioned ($D(H)$ is the domain of self-adj. of the Hamiltonian $H$). | |
| Feb 15, 2016 at 16:34 | history | answered | ACuriousMind♦ | CC BY-SA 3.0 |