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The time-independent Schrödinger equation Hψ = Eψ is of course an eigenvalue equation for the operator H. If H was a self-adjoint transformation on a finite-dimensional space then as is well known, there would only be a finite number of eigenvalues E for which the equation Hψ = Eψ had a non-trivial solution; however since H acts on an infinite-dimensional space, the situation can be more complicated. Indeed, H can have eigenfunctions ψ which lie in the domain L²(Rⁿ) of H (consisting of square-in
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The time-independent Schrödinger equation Hψ = Eψ is of course an eigenvalue equation for the operator H. If H was a self-adjoint transformation on a finite-dimensional space then as is well known, there would only be a finite number of eigenvalues E for which the equation Hψ = Eψ had a non-trivial solution; however since H acts on an infinite-dimensional space, the situation can be more complicated. Indeed, H can have eigenfunctions ψ which lie in the domain L²(Rⁿ) of H (consisting of square-in
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