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研究所、轉學考(插大)-近代物理學
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110年 - 110 國立中央大學_碩士班招生考試_光電類：近代物理#103854
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題組內容
6. For a simple harmonic potential well V(x)=k(X-X
0
)
2
/2,
(a) (5 pts) When a particle with a mass of m is in the well, what are the average values of the lowest kinetic and potential energies?
其他申論題
2. (10 pts) Consider the following set of ions:. To which ones can we apply Bohr's quantized energy formula? Explain your reasoning.
#439394
3. (10 pts) Consider a particle in a box (a.k.a. the infinite square well) with a length of L. Calculate the probability that a particle, in the ground state, will be found within the position from L /4 L to 3 L /4.
#439395
4. (10 pts) The 2nd bound state (n = 1) wave function of the harmonic oscillator is given by: Is the wave function normalized? Explain your reasoning
#439396
5. (10 pts) A lightbulb that is operated at 60 W actually produces about 3 W of visible light. Most of the rest of the energy is heat. Assume the average wavelength of visible light is 550 nm. Evaluate how many visible photons such a lightbulb produce each second.
#439397
(b) (5 pts) When a particle with a mass of m is in the well, what is the root-mean- square speed at the first excited state?
#439399
(c) (10 pts) If 20 fermions with a mass of m are in the well, what is the mean energy of fermion at absolute temperature T=0 K? What is the Ferni energy of the system?
#439400
(d) (5 pts) If 20 bosons with a mass of m are in the well, what is the total energy of bosons at absolute temperature T-0 K?
#439401
(a) (5 pts) When a particle is in an infinite square-well potential (V-＞∞), how does the lowest energy of the particle change when the potential V becomes finite.
#439402
(b) (10 pts) Continue (a), a particle is in a finite square-well potential as follows If the bottom of the square-well potential is increased from 0 to V', explain how the total energy and kinetic energy of the particle change?
#439403
8. (10 pts) Find the group and phase velocities of 10-MeV electrons.
#439404
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