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25. Matt:Hi, Alice. How are you?Alice:Not so good. I don’t feel very well.Matt:_____________________________(A) That’s wonderful. (B) You are sorry.(C) That’s too bad. (D) I’m glad to know that.

27. Alan:We are going to play in the championship final next Saturday.Lisa:______________________(A) It’s my treat! (B) I don’t know.(C) I need a farm. (D) Wow! I wish you good luck in the final.

28. Albert:_____________________Elissa:Oh, I see. I’ll add you later.(A) See you tomorrow. (B) Merry Christmas!(C) I just sent a friend request to you on Facebook. (D) I am full.

13. Consider a free electron gas in $d$ spatial dimensions. Let $n$ be the electron number density (defined as the number of electrons per unit length, area, or volume, depending on the dimension). Which of the following correctly describes the dependence of the Fermi energy $E_{F}$ on the density $n$? (A) $E_{F}\propto n^{2 / d}$ (B) $E_{F}\propto n^{d / 2}$ (C) $E_{F}\propto n$ (D) $E_{F}\propto n^{2}$ (E) $E_{F}\propto n^{1 / d}$

14. Consider a spinless particle in a three-dimensional isotropic simple harmonic oscillator potential. The particle is in an energy eigenstate with eigenenergy: $$ E = \left(99 + \frac{3}{2}\right) \hbar \omega $$ What is the degeneracy of this energy level? (A) 2500 (B) 5151 (C) 10100 (D) 100 (E) 5050

15. The total wavefunction of two electrons is written as a product of a spatial part $\psi(\vec{r}_1, \vec{r}_2)$ and a spin part $\chi_{spin}(s_1, s_2)$. Which of the following combinations correctly describes the symmetry of the spatial and spin parts specifically for the ground state of helium? (A) Spatial part is symmetric; Spin part is antisymmetric. (B) Spatial part is symmetric; Spin part is symmetric. (C) Spatial part is antisymmetric; Spin part is symmetric. (D) Spatial part is antisymmetric; Spin part is antisymmetric. (E) The Pauli principle forbids two electrons from occupying the same 1s spatial orbital, regardless of spin state.