![]() | 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 ˆHψ=iℏ˙ψ 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 ψ=ψ(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 ˆHψ=iℏ˙ψ 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 ψ=ψ(x,t)=X(x)T(t)
UPDATE: This method works pretty for such equations well since the equations reduce to ˆHX=EX and ˙T=E/(iℏ)T and the algorithm is very simple.