[领域] 量子力学，狭义相对论 (题目相关领域) [来源] 期中考试的一些题目 (课本习题、考古题、参考书...) [题目] 1.(Lorentz Transformation) Lorentz transformation in the x-direction can be capturde by a 2x2 matrix [ γ -γu ] [-γu γ ] where γ=1/√((1-u)^2) and u is the relative velocity between two inertia frames. For simplicity, I have set the speed of light to be unity c=1. For a particle moving at velocity v in the (x,t) frame, find its corresponding velocity v' in the (x',t')frame by the reduced Lorentz matrix in above. 2.(Relativistic Electrons) The kinetic energy of a relativistic electron is described by the 4x4 matrix k= [ mI σ‧P ] [σ‧P mI ] where I is the identity matrix of dimension two and the Pauli matrices σ are σx=[ 0 1 ] σy=[ 0 -i ] σz=[ 1 0 ] [ 1 0 ] [ i 0 ] [ 0 -1 ] The rest mass of motion of the electron is m and its momentum in P=(px,py,pz). (a)Bring the kinetic matrix k to diagonal form and find out the corresponding energies. (b)Choose the coordinate system so that the electron is moving along the positive z-axis. Find all eigenstates for a relativistic electron in motion. [瓶颈] (写写自己的想法，方便大家为你解答) 1.我不知道如何下手啊= =+ 2.我虽然已经算出来这个矩阵对角化的形式，但是不知道後面到底在讲些什麽... --

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