[題目] 兩個問題
[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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