Quantum mechanics, eigenfunctions!

posted by .

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! -

    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! -

    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.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    Eliminate the parameter (What does that mean?
  2. physics - quantum mechanics

    hi can you please help me with this particular question?
  3. english: crit. thinking

    Over time, non-specialists are usually able to assimilate radically new scientific ideas, even though these ideas may seem strange when they are initially introduced. Such was the case with Newtonian physics; when Newton proposed his …
  4. critical thinking

    Over time, non-specialists are usually able to assimilate radically new scientific ideas, even though these ideas may seem strange when they are initially introduced. Such was the case with Newtonian physics; when Newton proposed his …
  5. CRT205 Quiz

    Over time, non-specialists are usually able to assimilate radically new scientific ideas, even though these ideas may seem strange when they are initially introduced. Such was the case with Newtonian physics; when Newton proposed his …
  6. English

    Over time, non-specialists are usually able to assimilate radically new scientific ideas, even though these ideas may seem strange when they are initially introduced. Such was the case with Newtonian physics; when Newton proposed his …
  7. Critical Thinking

    Over time, non-specialists are usually able to assimilate radically new scientific ideas, even though these ideas may seem strange when they are initially introduced. Such was the case with Newtonian physics; when Newton proposed his …
  8. Critical Thinking

    Over time, non-specialists are usually able to assimilate radically new scientific ideas, even though these ideas may seem strange when they are initially introduced. Such was the case with Newtonian physics; when Newton proposed his …
  9. Quantum mechanics, eigenvalues, eigenfunctions

    What exactly is an eigenvalue? "To be an eigenfunction, the operator has to reproduce the function with some multiplicative constant." Is the eigenvalue the multiplicative constant -or- is it the m constant and the function?
  10. College algebra!

    For the linear function f(x) = 5x + 3 (a) Determine the slope and y-intercept (b) Use the slope and y-intercept to graph the linear function. (c) Determine the average rate of change of the function (d) Determine whether the linear …

More Similar Questions