Do all of the following problems. Show your work.
1) Consider the operator à = d²/dx² (the second derivative operator). For each of the following
functions f(x) determine whether or not the function is an eigenfunction of the operator Ă. For
cases where f(x) is an eigenfunction, give the corresponding eigenvalue.
a) f(x) = exp(ax), where a is a positive constant
b) f(x) = x exp(ax), where a is a positive constant
c) f(x) = sin(ax), where a is a positive constant
d) f(x) = sin(ax)cos(ax), where a is a positive constant.