複選題

17. A beam of neutrons is traveling at a speed of $v = 800 \, \mathrm{m/s}$ and is directed through a single slit of width $a = 1.0 \, \mu \mathrm{m}$. Given the Planck's constant $h = 6.626 \times 10^{-34} \, \mathrm{J} \cdot \mathrm{s}$ and the neutrons have mass $m_{n} = 1.675 \times 10^{-27} \, \mathrm{kg}$. Consider the neutrons as free quantum particles and their wave-like behavior. Which of the following statements are correct?
(A) The de Broglie wavelength of the neutrons is approximately $4.945 \times 10^{-10} \, \mathrm{m}$.
(B) The first minimum of the diffraction pattern on a screen far away from the slit occurs at an angle $\theta$ given by $\sin \theta = \lambda / a$.
(C) The phase velocity of the neutron wave is greater than the speed of particles.
(D) The group velocity of the neutron wave packet is equal to the speed of the particles.
(E) The uncertainty in the neutron's transverse momentum due to the slit is approximately $6.63 \times 10^{-28} \, \mathrm{kg} \cdot \mathrm{m/s}$.