110年 - 110 國立政治大學_碩士暨碩士在職專班招生考試_應用物理所:近代物理#102925

1.1 [6 points] Describe briefly the Stem-Gerlach experiment for the measurement of the magnetic moments of atoms, and discuss the significance of the results.

1.2 [4 points] Explain Larmor precession.

1.3[5 points] Which of the following are characteristics about the quantum harmonic oscillator? Choose all that apply.
I. Evenly spaced energy states
Ⅱ. The potential energy function is symmctric about the origin in the position coordinate
Ⅲ. The ground state has zero kinetic energy
Ⅳ. The probability of finding the particle outside the classically ailowed range is nonzero
V. The ground state energy is zero

1.4[4 points] For a single quantum barmonic oscillator that has an angular frequency w. At temperature T, what is the partition function?

1.5 [6 points] Write down the distribution f function for photons and fermions, respectively.

1.6[4 points] In an experimental observation of the photoelectric effect, docs increasing the light amplitude change the stopping potcntial?

1.7 [5 points] What is the physical interpretation of the horizontal intercept?

1.8 [6 points] What is physical interpretation of the slope of the line?

2.1 [ 10 points] Sketch and determine the constant A in terms of a, b.

2.2 [ 10 points] What is the probability of finding the particle to the left of a? b-a

3.[10 points] An electron has a speed v=0.85 c , c is the speed of light. Find its total energy and kinetic energy in electron volts.

4.[10 points] A free particle of mass m and energy E is moving from x = -∞ to x =∞. There is a potential stcp V, where V ＜ E, for x ≥0. Find the transmission and reflection coeficients for the particle in the one-dimensional step potential.

5.1[10 points] Calculate the highest energy level (called Fermi energy) ef of the electron in the metal in terms of N, V and m.

5.2 [10 points] What is the total energy of all the N electrons in the metal as expressed in terms of N and? What is the average electron energy?

110年 - 110 國立政治大學_碩士暨碩士在職專班招生考試_應用物理所:近代物理#102925

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