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 .

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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.

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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.

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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.

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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.

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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

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Answer 12

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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.

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Chapter 6 Solutions