Posted by **Steven** on Thursday, October 8, 2009 at 9:30pm.

Determine if the function sin(x)*e^(ax) where a=constant is an eigenfunction of the operators d/dx and d^2/(dx)^2

Okay. My understanding is that you use the operator and perform its "thing" on the function. In this case, you will have to find the 1st derivative of sin(x)*e^(ax) ... And if the result is sin(x)*e^(ax) multiplied by some constant, it is an eigenfunction.

Is this correct? I am doing the first derivative but it doesn't show up as an eigenvalue. Neither does the 2nd derivative :(

- Quantum mechanics, eigenfunctions! -
**DrPhysics**, Thursday, October 8, 2009 at 10:05pm
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 get back to sine. The problem says "determine if" so you can just say no. :)

- Quantum mechanics, eigenfunctions! -
**Steven**, Thursday, October 8, 2009 at 10:50pm
Thank you! I thought I was going crazy because I wasn't able to an eigenfunction since 1st deriv. would be

= cos(x)*e^(ax) + a*sin(x)*e^(ax)

which is definitely not an eigenfunction of the operator.

## Answer This Question

## Related Questions

- Quantum mechanics, eigenvalues, eigenfunctions - What exactly is an eigenvalue...
- math - Eliminate the parameter (What does that mean?) and write a rectangular ...
- College algebra! - For the linear function f(x) = 5x + 3 (a) Determine the slope...
- physics - quantum mechanics - hi can you please help me with this particular ...
- Calc - 1. Differentiae each function a) Y=-3x^2+5x-4 b) F(x) = 6/x-3/x^2 c) F(x...
- phys - 1) Pf(x)= f(-x), p operator Find the eigenvalues and eigenfunction of p ...
- Calculus - Consider the function f(x)=sin(1/x) Find a sequence of x-values that ...
- Calculus - Consider the function f(x)=sin(1/x) Find a sequence of x-values that ...
- calculus - Given f(x)=sin(x)-2cos(x) on the interval [0,2pi]. a) Determine where...
- Calculus - How do I graph sin and cosin example: graph y=-4sin(x + 3.14) Your ...

More Related Questions