1. A quantum model of a diatomic molecule. The simplest model of a diatomic molecule consists of two balls (atoms) connected by a spring obeying Hook's law (this model is commonly referred to as the harmonic oscillator). According to quantum mechanics, the vibrational energy of such a contraption can only take on discrete values, En = w(n + 3), where n = 0,1,2,3 ... is any non-negative integer. Here z 1.0 x 1034) xs is Planck's constant and w is the oscillation frequency of the molecule. This is all you need to know about quantum mechanics for the purpose of solving this problem. = 0 1-x a A. Assuming that the frequency w is known and that the molecule's surroundings are at temperature T, derive a formula describing the vibrational partition function q(T) = 2n=o e-En/(kb7) as a function of temperature [Note: the following identity may be useful: 1 + x + x2 + ... =; for 0