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研究所、轉學考(插大)-近代物理學
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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
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題組內容
4.
(b) When L is large, show that you can construct the (nearly) orthonormal eigenstates of the free particle from
(10%)
其他申論題
(a) Write down the wave function (x.t). (10%)
#442598
(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%)
#442599
(c) Calculate the expectation value of the energy in the state Y(xr,r) above. (5%)
#442600
(a) Can the free particle wave function be normalized in a box with size L?(10%)
#442601
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%)
#442603
(a) Please explain what a recursive function is. (6%)
#442604
(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%)
#442605
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%)
#442606
(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%)
#442607
(b) Consider another sum-of-subsets problem with n = 4, W =13, and w1= 3, w2 = 4, w3 = 5, w4 = 6. Use a similar tree as above, give a strategy to avoid searching every possible traversing route in the tree, and show that it can still get to the correct answer. (10%)
#442608
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