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 | 1 | initial version |
Thank you very much! I would like to wonder if there is extensive documentation on PDEs with sage (even with hundreds of lines of code). I am particularly interested in solving time dependent Schroedinger Equations that in one dimension (for example) have the form $$\hat H \psi = i\hbar \dot \psi$$ meaning that the wavefunction depends on x (space) and t (time). However in simpler forms (where for example the potential energy is 0) then the solution can be expressed as a product of two functions (like in the heat equation) as $\psi = \psi (x,t) = X(x)T(t)$
| | 2 | No.2 Revision |
Thank you very much! I would like to wonder if there is extensive documentation on PDEs with sage (even with hundreds of lines of code). I am particularly interested in solving time dependent Schroedinger Equations that in one dimension (for example) have the form $$\hat H \psi = i\hbar \dot \psi$$ meaning that the wavefunction depends on x (space) and t (time). However in simpler forms (where for example the potential energy is 0) then the solution can be expressed as a product of two functions (like in the heat equation) as $\psi = \psi (x,t) = X(x)T(t)$
UPDATE: This method works pretty for such equations well since the equations reduce to $\hat H X = EX$ and $\dot T = E/(i \hbar ) T$ and the algorithm is very simple.
