# hw11 - Homework 11 Prob 11.1 Consider two canonical systems...

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Unformatted text preview: Homework 11 Prob. 11.1 Consider two canonical systems that are initially in respective equilibrium at different temperature T 1 and T 2 and µ 1 and µ 2 . They are brought to contact at t = 0. (a) How does the entropy of the total system change at t = 0? (This is actually one of the definition of time) (5 pts) (b) If T 1 > T 2 and µ 1 = µ 2 for t < 0, describe the exchange between the two systems for t ≥ 0. When will the exchange stop? (5 pts) (c) If T 1 = T 2 and µ 1 > µ 2 for t < 0, describe the exchange between the two systems for t ≥ 0. When will the exchange stop? (5 pts) Prob. 11.2 For a 3D particle in the 3D simple harmonic oscillator described by: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 z y x r m z y x m z y x z y x m z y x m z y x H o o , , 2 1 , , 2 , , 2 1 , , 2 , , ˆ 2 2 2 2 2 2 2 2 2 2 ψ ϖ ψ ψ ϖ ψ ψ + ∇- = + + + ∇- = The energy eigenvalues are: + = + + + = 2 3 2 3 n n n n E z y x n ϖ ϖ , where 2 3 ϖ is referred to as the “zero-point energy” (okay, I know this name was twisted in the movie of “The...
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hw11 - Homework 11 Prob 11.1 Consider two canonical systems...

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