[領域] 量子力學，狹義相對論 (題目相關領域) [來源] 期中考試的一些題目 (課本習題、考古題、參考書...) [題目] 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. [瓶頸] (寫寫自己的想法，方便大家為你解答) 1.我不知道如何下手啊= =+ 2.我雖然已經算出來這個矩陣對角化的形式，但是不知道後面到底在講些什麼... --

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