Homework Set # 5 - Due October 1

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     1)  4.1.8  

     2)  4.1.9

     3)  4.1.10  

     4)  4.1.11

     5) The exponential in a plane wave is exp[i(k.r-ωt)].   We recognize x^μ=(ct,x¹,x²,x³) as a prototype vector in Minkowski space. If ωt-k.r is a scalar under a Lorentz transformation, show that k^μ=(ω/c,k¹,k²,k³) is a vector in Minkowski space. Hint: in Minkowski space the metric tensor g^μν=diag(1,-1,-1,-1). Note: Multiplication by ħ yields (E/c,p) as a vector in Minkowski space.

Solution

     6)  4.2.1

     7)  2.1.8

     8)  2.1.9