** Nobel Prize wining Physicist Gerard 't Hooft gave an outstanding road map how to become a good Theoretical Physicist. Have a look at it...**

** Nobel Prize wining Physicist Gerard 't Hooft gave an outstanding road map how to become a good Theoretical Physicist. Have a look at it...**

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**QUESTION:**

**A particle moving in one dimensions has energy**

** **

**where and denote the generalized coordinate and momentum.**

**Show that heat capacity of a gas comprising of such particles is**

**SOLUTION:**

The single particle partition function can be written as

Now,

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Two Useful Integration:

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,