The dynamics of a free relativistic particle of mass m is governed by the Dirac Hamiltonian H=c\vec{\alpha }\cdot \vec{p}+\beta m{c}^{2}, where \vec{p} is the momentum operator and \vec{\alpha }=\left( {\alpha }_{x},{\alpha }_{y},{\alpha }_{z} \right) and \beta are four 4\times 4 Dirac matrices. The acceleration operator can be expressed as

KG and Dirac equation — CSIR Net PYQ (Question 1)

A KG and Dirac equation previous-year question (PYQ) from Quantum Mechanics (CSIR Net). Read the question, check the correct answer, then practise the full topic.

Question 1 of 1 · 5.0 marks

The dynamics of a free relativistic particle of mass

m

is governed by the Dirac Hamiltonian

H = c α \cdot p + β m c^{2}

, where

p

is the momentum operator and

α = (α_{x}, α_{y}, α_{z})

and

β

are four

4 \times 4

Dirac matrices. The acceleration operator can be expressed as

1 $\frac{2 i c}{ℏ} (c p - α H)$
2 $2 i c^{2} α β$
3 $\frac{i c}{ℏ} H α$
4 $- \frac{2 i c}{ℏ} (c p + α H)$

Correct answer: Option 1

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