110年 - [非官方正解]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

1.(5%) De Broglie stated mathematically the equation for the frequency f and wavelength of electron wave λ. Which one is the equation that are referred to as the de Broglie relations (where E is the total energy, h is thhe Planck's constant, and p is the momentum): (A) (B)(C)(D) (E)

2.(5%)Which of the followings show the energy and momentum operators in quantum mechanics?(A) (B)(C) (D) (E)

4.(5%) Which of the following shows the Bose-Einstein distribution function, where C is a constant, k is the Boltzmann constant, and T is the temperature? (A)(B)(C)(D)(E)

5.(5%) In one dimension, the Schrodinger equation for an electron with Coulomb potential energy

.One simple function that satisfies the

required boundary conditions is. Find the normalization constant A for a particle

trapped in the 1D Coulomb potential energy in the range  (A)(B)(C)(D)(E)

6. (5%) A single crystal of table salt (NaCl) is irradiated with a beam of X rays of wavelength 0.250 nm, and the first Bragg reflection is observed at an angle of 300. What is the atomic spacing of NaCl? (A) 0.250 (B) 0.5 (C) 0.125 nm (D) 0.250 nm (E) 0.500 mm. 

(c) (5%) An electron with a kinetic energy of 100 eV, which is much less than the rest energy

(c) (6%) Evaluate the probability to find the particle in an interval of width 0.02L at x = -L/4 (that is, between x = -0.24L and x = -0.26L. (No integral is necessary for this calculation.

Charge of electron: 

Mass of electron: 
 Planck constant: