Solve a single PDE?

GROUPS:
 Hi there, i've been doing some quantum mechanics and I wanted to solve the time dependent Schrodinger equation in 1 spacial dimension with a periodic potential in time, yet whenever I use Mathematica's DSolve tool, I get the same argument that I input as an output.. my argument goes as follows: A=-6.104263*10^-39 ; B= i*6.625*10^-34 ; s=DSolve[ {A*D[\[Ψ][x,t],x,x]+Sin[2\[Pi]*t]*\[Ψ][x,t]+B*D[\[Ψ][x,t],t]==0 ,\[Ψ][0,t]==0, \[Ψ][0.005,t]==0},\[CapitalPsi],{x,t}] I've even set a boundary condition, I just don't know what I'm doing incorrectly
1 year ago
6 Replies
 I guess you need NDSolve since you are having numerical constants in your equations
1 year ago
 using the exact same code?
1 year ago
 Something like: A=-6.104263*10^-39;B=I*6.625*10^-34; s=NDSolve[{A*D[\[CapitalPsi][x,t],x,x]+Sin[2\[Pi]*t]*\[CapitalPsi][x,t]+B*D[\[CapitalPsi][x,t],t]==0,\[CapitalPsi][0,t]==0,\[CapitalPsi][0.005,t]==0},\[CapitalPsi][x,t],{x,0,0.005},{t,0,1}] note also that imaginary i is capital I in Wolfram Language
 Sander Huisman 1 Vote A=-6.104263*10^-39;B=I*6.625*10^-34; out=NDSolve[{A*D[\[CapitalPsi][x,t],x,x]+Sin[2\[Pi]*t]*\[CapitalPsi][x,t]+B*D[\[CapitalPsi][x,t],t]==0,\[CapitalPsi][0,t]==0,\[CapitalPsi][0.005,t]==0},\[CapitalPsi],{x,0,0.005},{t,0,1}] sol=\[CapitalPsi]/.First[out] Plot3D[Im[sol[x,t]],{x,0,0.005},{t,0,1},WorkingPrecision->100] As you can see the solution is kinda boring; it is zero everywhere. That's because your boundary conditions are 0...