Question

3. (20 points) A particle of mass m and energy E moving in a region where there is initially no potential energy encounters a potential dip of width L and depth U = -U0 U(x) = { 0, x <= 0, Region I; -U0, 0 < x < L, Region II; 0, x >= L, Region III Take the incident wave to be a plane wave and derive, including all algebraic steps, the reflection probabilities. (a) Draw the potential diagram. (b) Write the form that the Schrodinger equation takes in each region. (c) Write the form of the wave function in each region. (d) List the boundary conditions. (e) Solve the refection probability (as a function of E and U0)

          3. (20 points) A particle of mass m and energy E moving in a region where there is initially no potential energy encounters a potential dip of width L and depth U = -U0
U(x) = { 0, x <= 0, Region I; -U0, 0 < x < L, Region II; 0, x >= L, Region III
Take the incident wave to be a plane wave and derive, including all algebraic steps, the reflection probabilities.
(a) Draw the potential diagram.
(b) Write the form that the Schrodinger equation takes in each region.
(c) Write the form of the wave function in each region.
(d) List the boundary conditions.
(e) Solve the refection probability (as a function of E and U0)

3. (20 points) A particle of mass m and energy E moving in a region where there is initially no potential energy encounters a potential dip of width L and depth U = -U0
U(x) = 0, x <= 0, Region I; -U0, 0 < x < L, Region II; 0, x >= L, Region III
Take the incident wave to be a plane wave and derive, including all algebraic steps, the reflection probabilities.
(a) Draw the potential diagram.
(b) Write the form that the Schrodinger equation takes in each region.
(c) Write the form of the wave function in each region.
(d) List the boundary conditions.
(e) Solve the refection probability (as a function of E and U0)

Added by Elisa S.

Modern Physics

Kenneth S. Krane 3rd Edition

Chapter 5

Instant Answer

Solved by Expert Madhur L

05/25/2023

Step 1

(a) In Region I, the wave function takes the form f(x, y, z) = A exp(-i(x-xo)y-i(y-yo)z-i(z-zo)) Show more…

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3. A particle of mass m and energy E moving in a region where there is initially no potential energy encounters a potential dip of width L and depth U=-Uo U(x) = { 0, x <= 0, Region I; -Uo, 0 < x < L, Region II; 0, x >= L, Region III Take the incident wave to be a plane wave and derive, including all algebraic steps, the reflection probabilities. (a) Draw the potential diagram. (b) Write the form that the Schrodinger equation takes in each region. (c) Write the form of the wave function in each region. (d) List the boundary conditions. (e) Solve the reflection probability (as a function of E and Uo).