What kind of differential equation is the Schrodinger equation?

AxiomOfChoice
Messages
531
Reaction score
1
Does it have an easy classification (elliptic, hyperbolic, parabolic, for example)? Or does the fact that it has an "i" in it make this impossible?
 
Physics news on Phys.org
At least for time-independent potentials, the Schrodinger equation is formally equivalent to a diffusion equation (parabolic) via analytic continuation to imaginary times, so in that sense one could call it parabolic, but I'm not sure if Mathematicians have a reserved term to account for the fact that the solutions are complex numbers.
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
View full post »

Similar threads

I Classification of First Order Linear Partial Differential Eq
Replies
1
Views
2K
B Few basic questions about differential equations....
Replies
13
Views
2K
Insights Differential Equation Systems and Nature
Replies
14
Views
5K
I Why Is a Differential Equation Called Nonlinear?
Replies
3
Views
2K
I Why Lagrange’s method of solving Pp + Qq=R works?
Replies
3
Views
589
A Integrability of Systems of Differential Equations
Replies
5
Views
3K
B Basic Idea of Differential Equations
Replies
25
Views
3K
General solution vs particular solution
2
Replies
52
Views
7K
Numerical solution to Schrödinger equation - eigenvalues
Replies
1
Views
2K
A FEM basis polynomial order and the differential equation order
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top