Why did Schrodinger call his equation eigenvalue problem?

  • Thread starter kahoomann
  • Start date
  • #1
58
1

Main Question or Discussion Point

Why did Schrodinger call his equation eigenvalue problem?
We can solve Schrodinger equation since it's just differential equation with complex number
 

Answers and Replies

  • #2
Mute
Homework Helper
1,388
10
The Schrodinger equation is a separable PDE, and in separating the PDE you generate ODEs which are of the form of Sturm-Liouville differential Equations:

http://en.wikipedia.org/wiki/Sturm-Liouville_theory

Basically what the separated equations look like is

[tex]\mathcal{L}u = \lambda u[/tex]

where [itex]\mathcal{L}[/itex] is a linear differential operator acting on the function u and [itex]\lambda[/itex] is the eigenvalue, which is the separation constant introduced from separating the PDE. This is just a generalization, if you like, of the case in linear algebra, where the operator would be a matrix and u would be a vector. One difference between the two cases is that in linear algebra the eigenvalue spectrum is finite, whereas in the Sturm-Liouville theory it is generally infinite.
 
  • #3
8
0
eigen value problem

Dear friend i dont know much of physics,but to me,its called eigen value equation bcoz we can write it in simple form as
H(psi) = E(psi)
H being hamiltonian or total energy of system,and E being energy eigen value.
 

Related Threads for: Why did Schrodinger call his equation eigenvalue problem?

  • Last Post
2
Replies
39
Views
16K
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
16
Views
5K
Replies
1
Views
9K
Replies
1
Views
788
Top