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題組內容

4.

(a) Can the free particle wave function be normalized in a box with size L?(10%)

其他申論題

2. Explain the following subjects: (a) cosmic microwave background; (b) superconductors; (c) topological insulators; (d) gravitational wave. (5% each)

(a) Write down the wave function (x.t). (10%)

(b) You measure the energy of the particle at 1-=O. Write the possible values of the energy and the probability of measuring each. (10%)

(c) Calculate the expectation value of the energy in the state Y(xr,r) above. (5%)

(b) When L is large, show that you can construct the (nearly) orthonormal eigenstates of the free particle from (10%)

5. In a metal, the group velocity of a conducting carrier is is the dispersion relation or the band structure of the carrier. (Consider a simplified one dimensional case.) Show thatby a semi-classical approach, where F is the experienced force on the carrier. (10%)

(a) Please explain what a recursive function is. (6%)

(b) Write a recursive function sum(n) to return the summation of the sequence of consecutive integers from 1 to n using any programming language or pseudo- code.(10%)

2. (16%) Please propose an algorithm that can find the intersection between two arrays consisting of m and n integers respectively with time complexity better than O(mn) (8%) and analyze its time complexity. (8%)

(a) This tree can be used to find out all subsets of {W1, W2, W3}that sum to W(the sum-of-subscts problem); please explain what this tree represents and how it works to solve this problem. (6%)

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