Whats an “eigenvalue”?
They’re all over the place. The basic problem they solve is when you have a complicated system, you want to find the normal modes. i.e., two couple oscillators. The eigenvectors give you one symmetric and one anti-symmetric solution. In other words, they reparamterize your coordiate space. While they are important in classical physics, they are critical to quantum. They are also one of the two fundamental paradigms, known as matrix mechanics (the other is wave mechanics). All quantum operators are viewed as matrices acting on vectors, and eigenvectors for that operator tell you its quantum numbers. Eigenvalues are sometimes called “singular values” – because they’re the precise points where something interesting happens. (from Ron Resnick) An eigenvalue is a unique scalar which when it multiplies an eigenvector, produces a resultant vector equivalent to the operator of the eigen-equation applied to the same eigenvector. But you already knew that. Use in a sentence: Say what? • What is
