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The Dirac Equation — R. Shankar
Physics — Quantum Mechanics · dirac-equation-basics
Problem Show that the Dirac equation can be written in the form
i ℏ ∂ ψ ∂ t = H ψ i\hbar \frac{\partial \psi}{\partial t} = H\psi i ℏ ∂ t ∂ ψ = H ψ H = c α ⋅ p + β m c 2 H = c\boldsymbol{\alpha}\cdot\mathbf{p} + \beta mc^2 H = c α ⋅ p + β m c 2 α \boldsymbol{\alpha} α β \beta β 4 × 4 4\times 4 4 × 4 α i α j + α j α i = 2 δ i j , α i β + β α i = 0 , β 2 = 1. \alpha_i \alpha_j + \alpha_j \alpha_i = 2\delta_{ij}, \quad \alpha_i \beta + \beta \alpha_i = 0, \quad \beta^2 = 1. α i α j + α j α i = 2 δ ij , α i β + β α i = 0 , β 2 = 1. Browse the problem library