I just don\'t understand the math from step one to step twohere. I am trying to
ID: 690416 • Letter: I
Question
I just don't understand the math from step one to step twohere. I am trying to follow this derivation from beginning toend....I think the point is to derive epsilon. My only problem is that it's been four years since I tookmath. This looks to me like the second derivative of-(hbar)^2/2m. As I recall, hbar is a constant equal to 1.? x10^(-34). I think the 1st derivative would be -m^(-2), andthe 2nd derivative would be (m^(-3))/3. This is obviously notthe case, and I have no idea how the a even got in the denominatorof the 1st fraction in step 2. Can anyone explain this mathto me. how do I get from the left side to the right side inthis equation. They just left out too many steps for me tofollow.Explanation / Answer
-(hbar)^2/2m is the constant the d2/dx2 is taking the derivative of the cosine function The first derivative of cosine is -1*sine. You also need to takeinto account the chain rule, so a factor of n*pi/a comes out(since you are differentiating with respect to x) The derivative of sine is cosine. Also you need another factor ofn*pi/a by the chain rule. In the end you are returned the function cosine(n*pi*x/a), exceptit is scaled by a constant ( the eigenvalue) H*function =E*function. H = -(hbar)^2/2m d2/dx2 E = constants