9780030839931, Chapter 2, Problem 3P

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Chapter Problem 3P Problem The Classical Limit Dirac Statistics The distribution reduces provided that the function much less than unity for every positive that case must have (2.103) cessary is (2.104) that show that T) 1/2 (2.105) requires (2.106) condition the (b) significance length (2.107) (d Show that normalization constant appearing the velocity Step solution Step (a) assume equation the Ferm distribution the Maxwell distribution density Substitute Substitute 2m 2m Substitute such that and remains the same 2m substitute Therefore relation has been derived (b) For and using (2mk, that note the right hand side equation the Brogle wavelength electron having energy only when spacing fermions than apply he classical statistics gas as a, Substitute and and solve for approximately equal to (d) First, start with the relationship between and k, rearrange the term get function of 2m Step 5 Substitute "for appearing velocity distribution Substitute for distribution given by (1) Substitute distribution (m/A) (m/h) Substitute for Therefore relation derived Anonymous good solution