複選題

13. Which three of the following statements correctly describe the hydrogen atom, the harmonic oscillator, and the particle in a box in quantum mechanics?
(A) The energy quantization of a harmonic oscillator obtained from the Schrödinger equation reduces exactly to Planck's quantization formula; however, Max Planck did not provide a physical interpretation for this quantization.
(B) For a particle in a two-dimensional box, the numbers of ground and first excited states are identical as long as the box is square.
(C) For a harmonic oscillator, the ground-state energy satisfies the lower bound imposed by the Heisenberg uncertainty principle because its wavefunction is Gaussian.
(D) For the hydrogen atom, the principal quantum number specifies the total energy and the number of quantum states, while the spatial symmetry of the wavefunction must be further determined by the orbital and magnetic quantum numbers.
(E) In all three types of potentials, the wavefunction must vanish at infinity if the particles form a bound state under the influence of these potentials.