5. What is the energy carried by a photon with momentum ?
(A)
(B)
(C)
(D)
(E)

6. Which of the following distributions describes the statistical behavior of an ensemble of spin-1/2 identical particles at a low-temperature T? (kB is Boltzmann's constant and EF is Fermi energy.) (A)(B)(C) (D) (E)

7. Which of the following statements about superconductivity is correct? (A) All materials become superconducting below 30 K (B) The resistance of a superconductor is zero (C) Superconductivity violates the first law of thermodynamics (D) Superconductivity violates the second law of thermodynamics (E) All the above are incorrect

8. Which of the following pairs of Nobel laureates and their major reasons for being awarded is incorrect? (A) Niels Bohr --- atomic model (B) Louis de Broglie --- wave-particle duality (C) Albert Einstein --- quantum entanglement (D) John Bardeen --- superconductivity (E) Richard Feynman --- quantum electrodynamics

9. Which of the following discoveries did not contribute to the development of quantum mechanics? (A) Hydrogen spectrum (B) General relativity (C) Energy quanta (D) Wave-particle duality (E) All the above did

10. Which of the following is not a property of a laser? (A) High monochromaticity (B) High coherence (C) High directivity (D) High propagation speed (E) High intensity

11. If a quantum particle sees a potential shown in Figure 1 (a double-well potential), which of the following probability densities is most likely to be the ground state probability density? (A)(B)(C)(D) (E)

12. Given a particle with energy E in a finite potential U(x), as shown in Figure 2 (with regions I through V, where Region III has U ＞ E), what is the form of the particle's wavefunction in Region III? (A) ceκx, where κ ∈ ℝ (B) cx² (C) c₊eκx+ c₋e-κx, where κ ∈ ℝ (D) ce-κx, where κ ∈ ℝ (E) c₊sin(kx) + c₋cos(kx), where k ∈ ℝ

13. A photon is directed toward a stationary particle of mass m with momentum = pêx. After the collision, the photon reflects along the same path, i.e., = -p'êx. What is p'? (A) p (B)(C)(D) p - mc (E) 0

14. Which of the following masses is the smallest? (Hint: A neutron can decay into a proton, an electron, and an antineutrino.) (A) The mass of a Helium-4 atom (a stable atom consisting of two protons, two neutrons, and two electrons) (B) The total mass of an alpha particle (a helium ion consisting of two protons and two neutrons) and two electrons (C) The total mass of two protons, two neutrons, and two electrons (D) The total mass of one proton, three neutrons, and one electron (E) All the above are the same

15. What is the magnitude of the spin angular momentum of a spin-1/2 particle? (A) s = (B) s = (C) s = (D) s = (E) s = ℏ

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