Question

An eigenfunction of the operator d2/dx2
is Sin nx, where n = 1,2,3.... Find the
Corresponding eigenvalues​

Answer 1

To find its eigenfunction f, it is equivalent to solve Lf=λf, that is, d2fdx2=λf. This is an second order ODE with constant coefficient, which can be solved. After finding all the possible solutions for f, we can consider the normalized condition and initial conditions to find the specify f.

Answer 2

Eigen value is = -n² finally thanks