A two-level quantum system has energy eigenvalues
\( E_1 \) and \( E_2 \). A perturbing potential
\( H' = \lambda \Delta \sigma_x \) is introduced, where
\( \Delta \) is a constant having dimensions of energy,
\( \lambda \) is a small dimensionless parameter, and
\( \sigma_x = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} \).
The magnitudes of the first and the second order corrections to
\( E_1 \) due to \( H' \), respectively, are:
Consider a two-level system with energy states \( +\epsilon \) and \( -\epsilon \). The number of particles at \( +\epsilon \) level is \( N+ \) and the number of particles at \( -\epsilon \) level is \( N- \). The total energy of the system is \( E \) and the total number of particles is \( N = N+ + N- \). In the thermodynamic limit, the inverse of the absolute temperature of the system is:
(Given: \( \ln N! \approx N \ln N - N \))
Which of the following is an octal number equal to decimal number \((896)_{10}\)?
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