Title: From atoms to molecules to bands - Nico Reichholf

Q: What form has the simplified Laplacian for the case of a particle on a sphere?
- ∆ = ∂^2/∂r^2 + ∂/r*∂r + ∂^2/r^2∂phi^2
- ∆ = ∂^2/r^2∂phi^2 (correct)
- ∆ = ∂^2/∂r^2 + ∂/r*∂r

Q: What are the boundary conditions for the wavefunction for a particle on a ring?
- psi (phi + 2π) = psi (phi) (correct)
- psi (x + L) = psi (x)
- psi (phi + π) = psi (phi)

Q: Why is the Born-Oppenheimer approximation used?
- To solve the Schrödinger equation for molecules, with multiple coulomb interactions it is not possible to solve it analytically. (correct)
- To get a more precise nuclei distance in molecules, since those are considered stationary and the coulombic interactions constant.
- In order to ignore the electron wavefunctions when calculating the nuclei distance in molecules saving a lot of simulation time.

Q: What do we get with Born-Oppenheimer approximation?
- Energy in function of nuclei coordinates. (correct)
- Only the mean nuclei distance.

Q: Why can we use the Born-Oppenheimer approximation?
- Because the nuclei are almost stationary w.r.t. the electrons. (correct)
- Because the electron wavefunction does not depend on the coulombic potential generated by the nuclei.
- Because we are only interested in the coulombic repulsion between nuclei.

Q: How many quantum numbers do we get if we consider a particle on a sphere?
- 2: l and m_l (correct)
- 1: m_l
- 3: n, l and m_l

Q: Does the quantum number n influence the range of possible quantum numbers l?
- No
- Yes (correct)

Q: Does the quantum number n influence the range of quantum number m_l?
- Yes, m_l = -l, -l+1, ..., l
where l = 0, 1, ....,n-1 (correct)
- No, m_l and n do not depend on each other.
- No, m_l = -l, -l+1, ..., l
where l = h/(2π)*√s(s+1)

Q: How does the energy depend on the quantum number l in the case of a particle on a sphere?
- E = (h/2π)^2*l^2/(2mr^2)
  Hint: Is L2 = (h/2π)2*l(l+1) or L2 = (h/2π)2*l2 ?
- E = (h/2π)^2*l(l+1)/(2mr^2) (correct)
  Hint: Is L2 = (h/2π)2*l(l+1) or L2 = (h/2π)2*l2 ?

Q: For 3d transition metals, what is the rule
- Atom fill 4s before 3d
Ion fill 3d before 4s (correct)
- Atom fill 3d before 4s
Ion fill 4s before 3d