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題組內容

Part C. Calculations (Detailed calculation steps should be shown.)

12. An electron has a de Broglie wavelength of 1 pm. Please calculate its

(1) Kinetic energy,

其他申論題

8. Please draws the Allowed Projections of the orbital angular momentum of a state with / = 2. (Please specify their z components and the length of the vector .)

Part B. Please answer the questions "in detail".9. (1) Please define Zero-Point Energy (ZPE). (2) Please explain zero-point energy in terms of both (A) Harmonic oscillator and (B) A trapped particle in a one- dimensional box.

10. Please draw the (1) Potential well and Energy levels with specifying their ZPEs) and (2) Correlation between En and their quantum number of (A) Harmonic oscillator for n = 0 ~ 3 and (B) Infinite square well potential for n =1~ 3. (3) Please specify if their energy level intervals are equal?

11. How did Davisson and Germer prove the electron's wave property? (Please answer this question by simply drawing and explaining the experimental results, and prove the electron's wave property by using some relations/equations for its de Broglie wavelength from known or/and measured parameters.)

(2) Phasc velocity, and

(3) Group velocities of its de Broglie waves. (Relativistic effects should be considered.)

13.For a free particle, y = A eitbxw#, please calculate the Expectation Value of Momentum.

(1) Wavelength (nm),

(2) Frequency (Hz) and

(3) Energy (eV) of the electromagnetic wave emitted.

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