To show ψ ( z ) = C { e + α ( z + 1 2 L ) z < − 1 2 L cos k z cos ( 1 2 k L ) − 1 2 L < z < + 1 2 L e − α ( z − 1 2 L ) z > + 1 2 L or ψ ( z ) = C { e + α ( z + 1 2 L ) z < − 1 2 L − sin k z sin ( 1 2 k L ) − 1 2 L < z < + 1 2 L − e − α ( z − 1 2 L ) z > + 1 2 L .

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Answer 1

Question

Chapter 5, Problem 46E

To determine

To show ψ(z)=C{e+α( z+ 1 2 L) z<−12Lcoskzcos( 1 2 kL) −12L<z<+12Le−α( z− 1 2 L) z>+12L or ψ(z)=C{e+α( z+ 1 2 L) z<−12L−sinkzsin( 1 2 kL) −12L<z<+12L−e−α( z− 1 2 L) z>+12L .

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a) Consider two single-particle energy states of the fermion system, A and B, for which EA = μ- x and EB = μ + x. Show that the probability that state A is occupied is equal to the probability that state B is unoccupied. In other words, show that the Fermi and Dirac distribution, ƒ(E) 1 eß(E-μ) +1 is "symmetric" about the point E = μ. b) Write simplified, approximate expressions for f(E) when value of E is very close to μ. (i) E < µ, (ii) E» µ 2 and (iii) the

For each of the following sets of primitive lattice vectors, identify the Bravais lattice type and give the dimensions of the conventional unit cell in terms of a, b, and c: (a) (a/2)& + (a/2)§, ay, (a/V2)2; (b) (a/2)âx + (a/2)ŷ, aỹ, aĉ; (c) ax + 2bŷ, bŷ, c2; (d) ļax + }bŷ, bŷ, cê.

A) An atom has two electronic levels of energy 0 and. Suppose the atom is in thermal equilibrium with a heat bath at temperature T. What ensemble should be used for this atom? Calculate the partition function Z, the average energy E, and the Helmholtz free energy F for this atom in the canonical encapsulation. Find the probabilities of each microstate of the atom. B) Calculate the entropy S of this atom for the various methods given below. i) F = E-TS ii) Using the appropriate derivative of F. iii) Calculate (S -kn E: -P. In p.)using the microstate distribution probabilities.

Answer 2

Question

Chapter 5, Problem 46E

To determine

To show ψ(z)=C{e+α( z+ 1 2 L) z<−12Lcoskzcos( 1 2 kL) −12L<z<+12Le−α( z− 1 2 L) z>+12L or ψ(z)=C{e+α( z+ 1 2 L) z<−12L−sinkzsin( 1 2 kL) −12L<z<+12L−e−α( z− 1 2 L) z>+12L .

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Answer 3

Question

Chapter 5, Problem 46E

To determine

To show ψ(z)=C{e+α( z+ 1 2 L) z<−12Lcoskzcos( 1 2 kL) −12L<z<+12Le−α( z− 1 2 L) z>+12L or ψ(z)=C{e+α( z+ 1 2 L) z<−12L−sinkzsin( 1 2 kL) −12L<z<+12L−e−α( z− 1 2 L) z>+12L .

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Answer 4

Question

Chapter 5, Problem 46E

To determine

To show ψ(z)=C{e+α( z+ 1 2 L) z<−12Lcoskzcos( 1 2 kL) −12L<z<+12Le−α( z− 1 2 L) z>+12L or ψ(z)=C{e+α( z+ 1 2 L) z<−12L−sinkzsin( 1 2 kL) −12L<z<+12L−e−α( z− 1 2 L) z>+12L .

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Answer 5

Chapter 5, Problem 46E

To determine

To show ψ(z)=C{e+α( z+ 1 2 L) z<−12Lcoskzcos( 1 2 kL) −12L<z<+12Le−α( z− 1 2 L) z>+12L or ψ(z)=C{e+α( z+ 1 2 L) z<−12L−sinkzsin( 1 2 kL) −12L<z<+12L−e−α( z− 1 2 L) z>+12L .

Answer 6

Chapter 5, Problem 46E

To determine

To show ψ(z)=C{e+α( z+ 1 2 L) z<−12Lcoskzcos( 1 2 kL) −12L<z<+12Le−α( z− 1 2 L) z>+12L or ψ(z)=C{e+α( z+ 1 2 L) z<−12L−sinkzsin( 1 2 kL) −12L<z<+12L−e−α( z− 1 2 L) z>+12L .

Answer 7

Chapter 5, Problem 46E

To determine

To show ψ(z)=C{e+α( z+ 1 2 L) z<−12Lcoskzcos( 1 2 kL) −12L<z<+12Le−α( z− 1 2 L) z>+12L or ψ(z)=C{e+α( z+ 1 2 L) z<−12L−sinkzsin( 1 2 kL) −12L<z<+12L−e−α( z− 1 2 L) z>+12L .

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 5 - Prob. 1CQ Ch. 5 - Prob. 2CQ Ch. 5 - Prob. 3CQ Ch. 5 - Prob. 4CQ Ch. 5 - Prob. 5CQ Ch. 5 - Prob. 6CQ Ch. 5 - Prob. 7CQ Ch. 5 - Prob. 8CQ Ch. 5 - Prob. 9CQ Ch. 5 - Prob. 10CQ

To show ψ ( z ) = C { e + α ( z + 1 2 L ) z < − 1 2 L cos k z cos ( 1 2 k L ) − 1 2 L < z < + 1 2 L e − α ( z − 1 2 L ) z > + 1 2 L or ψ ( z ) = C { e + α ( z + 1 2 L ) z < − 1 2 L − sin k z sin ( 1 2 k L ) − 1 2 L < z < + 1 2 L − e − α ( z − 1 2 L ) z > + 1 2 L .

Solution Summary: The author enumerates the psi ((z)=Cle+alpha (z-12

To show ψ(z)=C{e+α( z+ 1 2 L) z<−12Lcoskzcos( 1 2 kL) −12L<z<+12Le−α( z− 1 2 L) z>+12L or ψ(z)=C{e+α( z+ 1 2 L) z<−12L−sinkzsin( 1 2 kL) −12L<z<+12L−e−α( z− 1 2 L) z>+12L .

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Chapter 5 Solutions

Solution Summary: The author enumerates the psi ((z)=Cle+alpha (z-12

To show ψ(z)=C{e+α( z+ 1 2 L) ​​​​​​​​ z<−12Lcoskzcos( 1 2 kL) −12L<z<+12Le−α( z− 1 2 L) z>+12L or ψ(z)=C{e+α( z+ 1 2 L) ​​​​​​​​ z<−12L−sinkzsin( 1 2 kL) −12L<z<+12L−e−α( z− 1 2 L) z>+12L .

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Chapter 5 Solutions

To show ψ(z)=C{e+α( z+ 1 2 L) z<−12Lcoskzcos( 1 2 kL) −12L<z<+12Le−α( z− 1 2 L) z>+12L or ψ(z)=C{e+α( z+ 1 2 L) z<−12L−sinkzsin( 1 2 kL) −12L<z<+12L−e−α( z− 1 2 L) z>+12L .