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Why did Schrodinger call his equation eigenvalue problem?

  1. Jun 10, 2008 #1
    Why did Schrodinger call his equation eigenvalue problem?
    We can solve Schrodinger equation since it's just differential equation with complex number
     
  2. jcsd
  3. Jun 10, 2008 #2

    Mute

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    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.
     
  4. Jun 11, 2008 #3
    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.
     
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