2L Suppose a barrier qualifies as wide, and its height and width are such that ² √2mU₁ transmission probabilities when E/U is 0.4 and when it is 0.6. (Ans: T=0.08 and 0.16) = 5. Calculate the
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- (1) A single particla quantum mechanical oscillator has energy levels (n + 1/2) hw, where n = 0, 1, 2, .. and w is the natural frequency of the oscillator. This oscillator is in thermal equi- librium with a reservoir at temperature T. (a) Find the ratio of probability of the oscillator being in the first excited state (n = 1) to the probability of being in the ground state. (b) Assuming that only the two states in Part la are occupied, find the average energy as a function of T. (c) Calculate the heat capacity at a constant volume. Does it depend on temperature?Problem 1: Consider a classical ideal gas in three dimensions, with N indistinguishable atoms confined in a box of volume N³. Assume the atoms have zero spin and neglect any internal degrees of freedom. Starting from the energy levels of a single atom in a box, find: (a) The Helmholtz free energy F' Hint: ſ. -ax² d.x e Va (b) The entropy o (c) The pressure pVerify the law of addition of quantum mechanical amplitude in case of neutron diffraction in single crystal.