Conditions for smoothness at regional boundaries for energy E less than barrier potential U 0 and verification that reflection coefficient B is expressed as A ( s i n h ( α L ) ( s i n h 2 ( α L ) + 4 α 2 k 2 / ( k 2 + α 2 ) 2 ) 1 2 ) e − i β .

Question

Want to see the full answer?

Answer 1

Question

Chapter 6, Problem 30E

(a)

To determine

Conditions for smoothness at regional boundaries for energy E less than barrier potential U0 and verification that reflection coefficient B is expressed as A(sinh( αL) ( sin h 2 ( αL )+ 4 α 2 k 2 / ( k 2 + α 2 ) 2 ) 1 2 )e−iβ .

(b)

To determine

Verification that reflection probability R in equation (6.16) is followed from this result.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

At what displacements is the probability density a maximum for a state of a harmonic oscillator with v = 1? (Express your answers in terms of the coordinate y.)

A free electron has a kinetic energy 13.3eV and is incident on a potential energy barrier of U =32.1eV and width w =0.091nm. What is the probability for the electron to penetrate this barrier (in %)? Check the correct answer and show all work

Show that the uncertainty in the momentum of a ground-state harmonic oscillator is (where h is h-bar, m is the mass, and k is the spring constant).

Answer 2

Question

Chapter 6, Problem 30E

(a)

To determine

Conditions for smoothness at regional boundaries for energy E less than barrier potential U0 and verification that reflection coefficient B is expressed as A(sinh( αL) ( sin h 2 ( αL )+ 4 α 2 k 2 / ( k 2 + α 2 ) 2 ) 1 2 )e−iβ .

(b)

To determine

Verification that reflection probability R in equation (6.16) is followed from this result.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 6, Problem 30E

(a)

To determine

Conditions for smoothness at regional boundaries for energy E less than barrier potential U0 and verification that reflection coefficient B is expressed as A(sinh( αL) ( sin h 2 ( αL )+ 4 α 2 k 2 / ( k 2 + α 2 ) 2 ) 1 2 )e−iβ .

(b)

To determine

Verification that reflection probability R in equation (6.16) is followed from this result.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 6, Problem 30E

(a)

To determine

Conditions for smoothness at regional boundaries for energy E less than barrier potential U0 and verification that reflection coefficient B is expressed as A(sinh( αL) ( sin h 2 ( αL )+ 4 α 2 k 2 / ( k 2 + α 2 ) 2 ) 1 2 )e−iβ .

(b)

To determine

Verification that reflection probability R in equation (6.16) is followed from this result.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 5

Chapter 6, Problem 30E

(a)

To determine

Conditions for smoothness at regional boundaries for energy E less than barrier potential U0 and verification that reflection coefficient B is expressed as A(sinh( αL) ( sin h 2 ( αL )+ 4 α 2 k 2 / ( k 2 + α 2 ) 2 ) 1 2 )e−iβ .

(b)

To determine

Verification that reflection probability R in equation (6.16) is followed from this result.

Answer 6

Chapter 6, Problem 30E

(a)

To determine

Conditions for smoothness at regional boundaries for energy E less than barrier potential U0 and verification that reflection coefficient B is expressed as A(sinh( αL) ( sin h 2 ( αL )+ 4 α 2 k 2 / ( k 2 + α 2 ) 2 ) 1 2 )e−iβ .

Answer 7

Chapter 6, Problem 30E

(a)

To determine

Conditions for smoothness at regional boundaries for energy E less than barrier potential U0 and verification that reflection coefficient B is expressed as A(sinh( αL) ( sin h 2 ( αL )+ 4 α 2 k 2 / ( k 2 + α 2 ) 2 ) 1 2 )e−iβ .

Answer 8

(b)

To determine

Verification that reflection probability R in equation (6.16) is followed from this result.

Answer 9

(b)

To determine

Verification that reflection probability R in equation (6.16) is followed from this result.

Answer 10

Expert Solution & Answer

Answer 11

Expert Solution & Answer

Answer 12

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 13

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

Conditions for smoothness at regional boundaries for energy E less than barrier potential U 0 and verification that reflection coefficient B is expressed as A ( s i n h ( α L ) ( s i n h 2 ( α L ) + 4 α 2 k 2 / ( k 2 + α 2 ) 2 ) 1 2 ) e − i β .

Solution Summary: The author explains the Schrödinger wave function and its spatial derivatives are continuous across the boundaries between three different regions. Smoothness conditions and reflection coefficient are determined from the principle of continuity.

Conditions for smoothness at regional boundaries for energy E less than barrier potential U0 and verification that reflection coefficient B is expressed as A(sinh( αL) ( sin h 2 ( αL )+ 4 α 2 k 2 / ( k 2 + α 2 ) 2 ) 1 2 )e−iβ .

Verification that reflection probability R in equation (6.16) is followed from this result.

Want to see the full answer?

Chapter 6 Solutions