IGNOU PHE 6 2018 - Consider a classical linear oscillator withε = p2/2m + bx2

Question

Consider a classical linear oscillator with

ε = p²/2m + bx²

^{where b is a constant. Assuming that the oscillator is in thermal equilibrium with a
heat reservoir at temperature T, calculate (i) the mean kinetic energy, (ii) the mean
potential energy for an assembly of N such oscillators.}

27 Jan 2018

Answer :

Word Count : 254

The problem describes a classical linear oscillator with the Hamiltonian: \[ \epsilon = \frac{p^2}{2m} + b x^2 \] where: - \( p \) is the momentum, - \( m \) is the mass, - \( x \) is the position, - \( b \) is a constant. The oscillator is in thermal equilibrium at temperature \( T \), meaning we can use the equipartition theorem to compute the mean kinetic and potential energies. ### (i) Mean Kinetic Energy The equipartition theorem

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