# Why did Schrodinger call his equation eigenvalue problem?

1. Jun 10, 2008

### kahoomann

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

2. Jun 10, 2008

### Mute

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

$$\mathcal{L}u = \lambda u$$

where $\mathcal{L}$ is a linear differential operator acting on the function u and $\lambda$ 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. Jun 11, 2008

### m-i-t-o

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.