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

Can someone help me

Need help on the following questions on biomechanics. (Please refer to images below)A gymnast weighing 68 kg attempts a handstand using only one arm. He plants his handat an angle resulting in the reaction force shown.A) Find the resultant force (acting on the Center of Mass)B) Find the resultant moment (acting on the Center of Mass)C) Draw the resultant force and moment about the center of mass on the figure below. Will the gymnast rotate, translate, or both? And in which direction?

Please help me on the following question (Please refer to image below)An Olympic lifter (m = 103kg) is holding a lift with a mass of 350 kg. The barexerts a purely vertical force that is equally distributed between both hands. Each arm has amass of 9 kg, are 0.8m long and form a 40° angle with the horizontal. The CoM for each armis 0.5 m from hand. Assuming the lifter is facing us in the diagram below, his right deltoidinserts 14cm from the shoulder at an angle of 13° counter-clockwise from the humerus.A) You are interested in calculating the force in the right deltoid. Draw a free body diagramof the right arm including the external forces, joint reaction forces, a coordinate system andstate your assumptions.B) Find the force exerted by the right deltoidC) Find the shoulder joint contact force. Report your answer using the magnitude and directionof the shoulder force vector.

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