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 .

Question

Want to see the full answer?

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 .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

A) An atom has two electronic levels of energy 0 and ɛ. 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.

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

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 .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

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 .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

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 .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

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

Expert Solution & Answer

Answer 9

Expert Solution & Answer

Answer 10

Want to see the full answer?

Check out a sample textbook solution

See solution

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 .

Want to see the full answer?

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 .

Want to see the full answer?

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 .