A quantum particle of mass is confined to free motion along a 1D segment of... · PHYSICS Dataset #6884

Physics · modern-physics

Problem

A quantum particle of mass mm is confined to free motion along a 1D segment of length aa. Using any approach you like, calculate the average force the particle exerts on the 'walls' (ends) of such '1D potential well' in thermal equilibrium, and analyze its temperature dependence, focusing on the low-temperature and high-temperature limits. Hint: You may consider the series Θ(ξ)≡∑n=1∞exp⁡{−ξn2}\Theta(\xi) \equiv \sum_{n=1}^{\infty} \exp \left\{-\xi n^{2}\right\} a known function of ξ.31\xi .{ }^{31}

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