複選題

Problem 12
Consider the ground state of an Al atom with Z=13. Find the correct descriptions:
(A) The electron configuration is: 1s² 2s² 2p⁶ 2d³.
(B) The magnitude of the angular momentumh.
(C) The magnitude of the sin angular momentums is
(D) The magnitude of the total angular momentumcan be

(E) The magnitude of the total angular momentumcan be

Problem 1What physical situation (in one dimension) does the following time-dependent Schrödinger equationdescribe?where k and e are real, non-zero constants.(A)A particle traveling up a ramp along the x-axis.(B) A particle in a finite square well potential.(C) A particle in an infinite square well potential.(D) An electron moving along the x-axis in the electric field of a proton at x=0.(E) None of the above.

Problem 2Find the correct statement:(A) The Fermi-Dirac distribution can be used to in the analysis of the properties of photons.(B) The peak wavelength of blackbody radiation is inversely proportional to temperature (1/T).(C) The spin of a photon is 1/2.(D) In a quantized system, each quantum state can only contain one photon.(E) At room temperature, the average kinetic energy of gas molecules is proportional to T2.

Problem 3Consider electron states of a particle in a finite quantum well, with the potential energy V(x) definedby V(0 ＜x ＜ W) = 0 in the well and V(x) = V0 ＞ 0 outside the well. Which of the statements is CORRECT?(A) An eigenstate in this case always describes a bound state in space.(B) The first excited state has an energy E1 with E1 ＜ Vo always.(C) The wave function of ground state can sometimes oscillate with nodal points where the wave function vanishes.(D) For any bound eigenstate in the system, the probability density is nonvanishing in the well and vanishing outside the well.(E) None of the above.

Problem 4Which quantum number (n, l, mi, ms) is not a possible set of a 2p electron?(A) (2, 1, +1, +1/2)(B) (2, 1, +1, -1/2)(C) (2, 1, 0, +1/2)(D) (2, 0, -1, +1/2)(E) (2, 1, -1, -1/2)

Problem 5According to band theory, beryllium, an alkaline earth metal, is predicted to behave as an insulator.However, it acts as a conductor due to:(A) The presence of a half-filled 2s band.(B) The overlap between the filled 2s band and the empty 2p band.(C) The presence of an empty 2p band.(D) The overlap between the filled 2p band and the empty 3s band.(E) The presence of a half-filled 3s band.

Problem 6 Consider the transmission of an incident electron with energy E through the one dimensional step potential barrier V(x) with V(x ＜ 0) = 0 outside the barrier, and V(x ＞ 0) = Vo in the barrier (V0 ＞ 0). Which of the following statements is CORRECT about the transmission coefficient T? (A) If the incident electron comes from x = +infinity, with E＞ V0,then the corresponding T = 1. (B) If the incident electron comes from x = - infinity, with E ＞V0, then the corresponding T = 1. (C) If the incident electron comes from x = - infinity, with E＜V0, then it has a nonvanishing probability in the barrier as well as T ＞ 0 due to quantum tunneling. (D) Replace V(x) by a potential barrier of finite width, with V(0 ＜ x ＜W) = Vo in the barrier and V(x) = 0 outside the barrier. An incident electron with E＜V0 has T ＞ 0 due to quantum tunneling. (E) None of the above.

Problem 7An electron is bound in a potential well. The wave function of the electron is:Y(x,t) = v(x)e-iEtn, where φ(x) is shown as below and E is a real number. Which one ofthe following potential wells would fit best to this wave function?(A)(B)(C)(D)(E)

Problem 8 A one-dimensional infinite potential well locating between -0.5 nm to 0.5 nm and contains 10 electrons. It has 10 electrons inside. What is the least energy, in eV, the incident light must have in order to excite a ground-state electron (i.e., at the lowest n quantum value) in this system to the lowest higher state it can occupy when T=0? (A) ~8.7 eV, (B) ~13.6 eV, (C) ~5.61 eV, (D) ~13.2 eV, (E) ~44.9 eV.

Problem 9In Bohr's hydrogen model, if the Coulomb interaction between the electron and the nucleus changes to a power-law potential: V(r) = krN, where k and N are positive constants. Applying Bohr's hypothesis to calculate the energy of hydrogen atom, the energy will be proportional to the quantumnumber n as(A)(B) (C)(D) , and (E) n-2.

Problem 10Which one of the following statements about free bosons, fermions, and classical particles is correct?(A) Bosons possess integer spin and follow the Maxwell-Boltzmann distribution in the low-temperature regime.(B) Fermions are indistinguishable particles that obey the Pauli exclusion principle and follow the FermiDirac distribution in all temperature range.(C) Classical particles can either be distinguishable or indistinguishable depending on the type of atoms or particles.(D) In the low-temperature limit, bosons and fermions cannot occupy the same quantum state, in contrast to classical particles.(E) In Bose-Einstein condensation, particles follow the Bose-Einstein distribution, with most particles occupying either the same excited state or the ground state. This phenomenon can be observed macroscopically.

115年 - 114 台灣聯合大學系統_碩士班招生考試_電機類:近代物理#137742

113年 - 113 台灣聯合大學系統_碩士班招生考試_電機類:近代物理#137735

110年 - 110 國立臺灣大學_碩士班招生考試_物理系天文物理所與應用物理所(三所聯招):近代物理學(A)#113053

110年 - 110 國立臺灣大學_碩士班招生考試_電子工程研究所丙組:近代物理(含半導體物理)#105749

110年 - 110 國立中山大學碩士暨碩士專班招生考試_物理系碩士班:近代物理#105698

110年 - 110台灣聯合大學系統_碩士班招生考試_電機類:近代物理#105578

110年 - 110 國立清華大學碩士班考試入學試題_聯合招生:近代物理#105281

110年 - 110台灣聯合大學系統_碩士班招生考試_物理類:近代物理#104513

110年 - 110 國立清華大學碩士班考試入學試題_生命科學院/丙組(計算生物與人工智慧組):近代物理#104511

110年 - 110 國立中央大學_碩士班招生考試_光電類：近代物理#103854