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Question: Can you help solution of the following PDE system

Question:Can you help solution of the following PDE system

Melvin Brown 124 Maple
differential-equation pde pdsolve
May 13 2019
1


I am unable to replicate solution of problem 169 below.  Can you help me debug?

Melvin Brown

Schrdiff(o(t), t, t)dinger PDE on (x,y,t) with initial and boundary conditions. Zero potential: problem number 169

 

Here is the problem 169 specification and solution from the Nasser list:

> 

restart

> 

with(PDEtools); with(CodeTools)

> 

x:='x';t:='t';y:='y';hbar:='hbar';

x

 

t

 

y

 

hbar

(1.1)
> 

interface(showassumed=0);

1

(1.2)
> 

pde:=I*diff(f(x,y,t),t)=-hbar^2*(diff(f(x,y,t),x$2)+diff(f(x,y,t),y$2))/(2*m);

I*(diff(f(x, y, t), t)) = -(1/2)*hbar^2*(diff(diff(f(x, y, t), x), x)+diff(diff(f(x, y, t), y), y))/m

(1.3)
> 

ic:=f(x,y,0)=sqrt(2)*(sin(2*Pi*x)*sin(Pi*y)+sin(Pi*x)*sin(2*Pi*y));

f(x, y, 0) = 2^(1/2)*(sin(2*Pi*x)*sin(Pi*y)+sin(Pi*x)*sin(2*Pi*y))

(1.4)
> 

bc:=f(0,y,t)=0,f(1,y,t)=0,f(x,1,t)=0,f(x,0,t)=0;

f(0, y, t) = 0, f(1, y, t) = 0, f(x, 1, t) = 0, f(x, 0, t) = 0

(1.5)
> 

cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve([pde,ic,bc],f(x,y,t))),output='realtime'));

memory used=159.58MiB, alloc change=102.00MiB, cpu time=4.37s, real time=4.23s, gc time=452.40ms

 

4.233

(1.6)
> 

with(plots); evalf(f(1, 2, 2))

f(1, 2, 2)

(1.7)
> 

plot3d(f(x, y, 3), x = -1 .. 1, y = -1 .. 1)

Warning, expecting only range variables [x, y] in expression f(x,y,3) to be plotted but found name f

 

 

The problem seems to fail... Why?

> 

``


 

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