Show that the stationary states can be written in the form ψ n ( x ) = 1 L e 2 π i n x / L , ( − L / 2 < x < L / 2 ) and the allowed energies are E n = 2 m ( n π ℏ L ) 2 .

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Answer 1

Question

Chapter 7.2, Problem 7.9P

(a)

To determine

Show that the stationary states can be written in the form ψn(x)=1Le2πinx/L, (−L/2<x<L/2) and the allowed energies are En=2m(nπℏL)2.

(b)

To determine

The first-order correction to En.

(c)

To determine

The good linear combinations of ψn and ψ−n and show that first-order correction can be determined with these states using Equation 7.9.

(d)

To determine

The hermitian operator A that fits the requirements of the theorem and show that the simultaneous eigenstates H0 and A are precisely the same used in part (c).

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Answer 2

Question

Chapter 7.2, Problem 7.9P

(a)

To determine

Show that the stationary states can be written in the form ψn(x)=1Le2πinx/L, (−L/2<x<L/2) and the allowed energies are En=2m(nπℏL)2.

(b)

To determine

The first-order correction to En.

(c)

To determine

The good linear combinations of ψn and ψ−n and show that first-order correction can be determined with these states using Equation 7.9.

(d)

To determine

The hermitian operator A that fits the requirements of the theorem and show that the simultaneous eigenstates H0 and A are precisely the same used in part (c).

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Answer 3

Question

Chapter 7.2, Problem 7.9P

(a)

To determine

Show that the stationary states can be written in the form ψn(x)=1Le2πinx/L, (−L/2<x<L/2) and the allowed energies are En=2m(nπℏL)2.

(b)

To determine

The first-order correction to En.

(c)

To determine

The good linear combinations of ψn and ψ−n and show that first-order correction can be determined with these states using Equation 7.9.

(d)

To determine

The hermitian operator A that fits the requirements of the theorem and show that the simultaneous eigenstates H0 and A are precisely the same used in part (c).

Expert Solution & Answer

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Answer 4

Question

Chapter 7.2, Problem 7.9P

(a)

To determine

Show that the stationary states can be written in the form ψn(x)=1Le2πinx/L, (−L/2<x<L/2) and the allowed energies are En=2m(nπℏL)2.

(b)

To determine

The first-order correction to En.

(c)

To determine

The good linear combinations of ψn and ψ−n and show that first-order correction can be determined with these states using Equation 7.9.

(d)

To determine

The hermitian operator A that fits the requirements of the theorem and show that the simultaneous eigenstates H0 and A are precisely the same used in part (c).

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Answer 5

Chapter 7.2, Problem 7.9P

(a)

To determine

Show that the stationary states can be written in the form ψn(x)=1Le2πinx/L, (−L/2<x<L/2) and the allowed energies are En=2m(nπℏL)2.

(b)

To determine

The first-order correction to En.

(c)

To determine

The good linear combinations of ψn and ψ−n and show that first-order correction can be determined with these states using Equation 7.9.

(d)

To determine

The hermitian operator A that fits the requirements of the theorem and show that the simultaneous eigenstates H0 and A are precisely the same used in part (c).

Answer 6

Chapter 7.2, Problem 7.9P

(a)

To determine

Show that the stationary states can be written in the form ψn(x)=1Le2πinx/L, (−L/2<x<L/2) and the allowed energies are En=2m(nπℏL)2.

Answer 7

Chapter 7.2, Problem 7.9P

(a)

To determine

Show that the stationary states can be written in the form ψn(x)=1Le2πinx/L, (−L/2<x<L/2) and the allowed energies are En=2m(nπℏL)2.

Answer 8

(b)

To determine

The first-order correction to En.

Answer 9

(b)

To determine

The first-order correction to En.

Answer 10

(c)

To determine

The good linear combinations of ψn and ψ−n and show that first-order correction can be determined with these states using Equation 7.9.

Answer 11

(c)

To determine

The good linear combinations of ψn and ψ−n and show that first-order correction can be determined with these states using Equation 7.9.

Answer 12

(d)

To determine

The hermitian operator A that fits the requirements of the theorem and show that the simultaneous eigenstates H0 and A are precisely the same used in part (c).

Answer 13

(d)

To determine

The hermitian operator A that fits the requirements of the theorem and show that the simultaneous eigenstates H0 and A are precisely the same used in part (c).

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

Ch. 7.1 - Prob. 7.1P Ch. 7.1 - Prob. 7.2P Ch. 7.1 - Prob. 7.3P Ch. 7.1 - Prob. 7.4P Ch. 7.1 - Prob. 7.5P Ch. 7.1 - Prob. 7.6P Ch. 7.2 - Prob. 7.8P Ch. 7.2 - Prob. 7.9P Ch. 7.2 - Prob. 7.10P Ch. 7.2 - Prob. 7.11P

Show that the stationary states can be written in the form ψ n ( x ) = 1 L e 2 π i n x / L , ( − L / 2 &lt; x &lt; L / 2 ) and the allowed energies are E n = 2 m ( n π ℏ L ) 2 .

Show that the stationary states can be written in the form ψn(x)=1Le2πinx/L, (−L/2<x<L/2) and the allowed energies are En=2m(nπℏL)2.

The first-order correction to En.

The good linear combinations of ψn and ψ−n and show that first-order correction can be determined with these states using Equation 7.9.

The hermitian operator A that fits the requirements of the theorem and show that the simultaneous eigenstates H0 and A are precisely the same used in part (c).

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Chapter 7 Solutions

Show that the stationary states can be written in the form ψ n ( x ) = 1 L e 2 π i n x / L , ( − L / 2 < x < L / 2 ) and the allowed energies are E n = 2 m ( n π ℏ L ) 2 .