Answer to Question #135600 in Physical Chemistry for May Chalermwat

Question

Is the function x^(k+1)y^(k+2) an eigenfunction of the operator x(d/dx) + y(d/dy) ? If it is, what is
the eigenvalues? What is the implication of this question in a quantum mechanical
context?

Answer 1

Such an equation, where the operator, operating on a function, produces a constant times the function, is called an eigenvalue equation. The function is called an eigenfunction, and the resulting numerical value is called the eigenvalue. Eigen here is the German word meaning self or own .