作者JohnMash (John)
看板Physics
标题Re: [问题] Dirac equation
时间Sat Dec 12 10:48:45 2009
※ 引述《chendaolong (JoJo A Go!Go!)》之铭言：
: Dirac equation:
: http://en.wikipedia.org/wiki/Dirac_equation
: Schroedinger equation 是非相对论的
: 如果要符合相对论要求(至少狭义相对论)
: 就必须要求方程式符合 covariant form
: Dirac equation 是符合 covariant form 其中之一
: 另一个较有名的则是 Klein–Gordon equation
: Dirac equation 如下
if you want to modify Schrodinger eq. (1st PDE) to
comply with special relativity,
you may assume
(R^k ∂_k) ψ=m ψ, where k=0,1,2,3
and we take h=c=1, and R^k is constant
Then
(R^i ∂_i) (R^k ∂_k) ψ=m^2 ψ, where i,k=0,1,2,3
if you want it become Klein-Gordon Eq.,
∂^k ∂_k ψ=m^2 ψ
you need
{R^i,R^k}=2 g^{ik}
Hence,
R^k CANNOT be a number, MUST be matrix.
Now you can use Pauli matrices to consruct R^k,
then you get Dirac Eq.
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