Quantum particles of unit mass, in a potential
\(V(x)=\left\{\begin{array}{cc} \frac{1}{2} \omega^2 x^2 & x>0 \\ \infty & x \leq 0 \end{array}\right.\)
are in equilibrium at a temperature T. Let n2 and n3 denote the numbers of the particles in the second and third excited states respectively. The ratio n2/n3 is given by
1
\(\exp \left(\frac{2 \hbar \omega}{k_B T}\right)\)
2
\(\exp \left(\frac{\hbar \omega}{k_B T}\right)\)
3
\(\exp \left(\frac{3 \hbar \omega}{k_B T}\right)\)
4
\(\exp \left(\frac{4 \hbar \omega}{k_B T}\right)\)