Recent content by pedroobv

I think that it is easy to show that the last sum is not zero because if it was zero that would mean that \phi = \psi_{1} according to the equations 1=\sum_{k}|a_{k}|^{2} \phi = \sum_{k}a_{k}\psi_{k} But as the problem statement says, \phi\neq \psi_{1}, so the sum can't be zero. So far, I...

But if the last sum is not zero that mean that there is a mistake somewhere since the purpose is to obtain \int \phi^{*} \hat{H} \phi d\tau>E_{1} right?

Homework Statement This is the problem 8.10 from Levine's Quantum Chemistry 5th edition: Prove that, for a system with nondegenerate ground state, \int \phi^{*} \hat{H} \phi d\tau>E_{1}, if \phi is any normalized, well-behaved function that is not equal to the true ground-state wave function...

Ok, thank you very much. That answers my question.

[SOLVED] Dirac delta function and Heaviside step function In Levine's Quantum Chemistry textbook the Heaviside step function is defined as: H(x-a)=1,x>a H(x-a)=0,x<a H(x-a)=\frac{1}{2},x=a Dirac delta function is: \delta (x-a)=dH(x-a) / dx Now, the integral: \int...

Ok thanks anyway, I already solved it. I forgot to take the absolute value.

Sorry, I made a mistake in the first equation. Instead of \frac{4|N|^{2}s^{2}}{l(s^{2}-b_{2})}\left(1-(-1)^{n}cos(bl)\right)dp Must be: \frac{4|N|^{2}s^{2}}{l(s^{2}-b^{2})^{2}}\left(1-(-1)^{n}cos(bl)\right)dp

[SOLVED] Probability for a momentum value for particle in a box Homework Statement This is the problem 7.37 from Levine's Quantum Chemistry Textbook. Show that, for a particle in a one-dimensional box of length l, the probability of observing a value of p_{x} between p and p+dp is...