The Hamiltonian for a spin- \frac{1}{2} particle at rest is given by H={E}_{0}\left( {\sigma }_{z}+\alpha {\sigma }_{x} \right), where {\sigma }_{x} and {\sigma }_{z} are Pauli spin matrices and {E}_{0} and \alpha are constants. The eigenvalues of this Hamiltonian are

Spin Angular momentum — CSIR Net PYQ (Question 1)

A Spin Angular momentum previous-year question (PYQ) from Quantum Mechanics (CSIR Net). Read the question, check the correct answer, then practise the full topic.

Question 1 of 13 · 3.5 marks

The Hamiltonian for a spin-

\frac{1}{2}

particle at rest is given by

H = E_{0} (σ_{z} + α σ_{x})

, where

σ_{x}

and

σ_{z}

are Pauli spin matrices and

E_{0}

and

α

are constants. The eigenvalues of this Hamiltonian are

1 $\pm E_{0} 1 + α^{2}$
2 $\pm E_{0} 1 - α^{2}$
3 $E_{0}$ (doubly degenerate)
4 $E_{0} (1 \pm \frac{1}{2} α^{2})$

Correct answer: Option 1

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