Quantum mechanics, eigenfunctions!
You are absolutely right. To be an eigenfunction, the operator has to reproduce the function with some multiplicative constant. Even without doing a lot of work, you can see for the special case of a=0 it doesn't work because you need to take four derivatives of sine to ...
October 8, 2009
This question is not well defined. By 'expi' do you mean exp(i)? In other words, is the expression [exp(i)]^i ? If so, then the answer is undoubtedly exp(-1). You can use Euler's equation to show this, but it is much easier to use this fact about exponents: (a^b)^c...
March 3, 2007