What Is the E/U Ratio for a Half Reflection Coefficient in Quantum Tunneling?

Click For Summary
SUMMARY

The discussion focuses on determining the ratio E/U for a half reflection coefficient (R = 1/2) in quantum tunneling scenarios. Key equations include the reflection coefficient formula R = (k1 - k2)^2 / (k1 + k2)^2, where k1 and k2 are wave numbers related to the particle's energy and the potential barrier height. The relationship between transmission and reflection is established through the equation Transmission + Reflection = 1, leading to the conclusion that the ratio can be derived from the defined variables in the equations. The challenge lies in isolating a numerical ratio without extraneous variables.

PREREQUISITES
  • Understanding of quantum mechanics concepts such as wave functions and potential barriers.
  • Familiarity with the reflection and transmission coefficients in quantum tunneling.
  • Knowledge of the variables involved, including energy (E), potential height (U), and mass (m).
  • Proficiency in manipulating exponential functions and algebraic expressions.
NEXT STEPS
  • Explore the derivation of the reflection coefficient in quantum mechanics.
  • Study the implications of the wave number (k) in quantum tunneling scenarios.
  • Investigate the relationship between energy levels and potential barriers in quantum systems.
  • Learn about the significance of the transmission coefficient and its applications in quantum physics.
USEFUL FOR

Students and researchers in quantum mechanics, particularly those studying quantum tunneling and barrier penetration phenomena. This discussion is beneficial for anyone looking to deepen their understanding of reflection and transmission in quantum systems.

PsychonautQQ
Messages
781
Reaction score
10

Homework Statement


A particle of energy E approaches a step barrier of height U. What should be the ratio E/U be so that the reflection coefficient is 1/2.


Homework Equations


Transmission + Reflection = 1
Transmission = e^(-2a*alpha)
a = mw∏/h
alpha^2 = (8m∏^2/h^2)(U-E)

Reflection = (k1-k2)^2 / (k1+k2)^2



The Attempt at a Solution


So this is a little bit messy.. I assume most people that are going to help me are familiar with these basic transmission and reflection equations. Anyway is there a possible way to solve this problem an get a ratio that is JUST a number? wouldn't you always have other variables in it since it's talking about a completely undefined particle? there are no ways to get the m's and w's out of the equations right?
 
Physics news on Phys.org
All those k's depend on energy.
Expand them out in the reflection coefficient and see what happens.
 

Similar threads

Correct Setup for Finite Difference to Calculate Quantum Tunneling
  • · Replies 2 ·
Replies
2
Views
1K
Quantum Tunelling Problem with Boundary Conditions
  • · Replies 3 ·
Replies
3
Views
3K
Classical behavior, 3 dimension wave function and reflection
  • · Replies 2 ·
Replies
2
Views
2K
E<V Potential Step Confusion
  • · Replies 7 ·
Replies
7
Views
3K
Tunneling with an alpha particle
  • · Replies 6 ·
Replies
6
Views
6K
Calculating Quantum Tunneling Probability - 1.524 eV, 343 pm, 2.654 eV
  • · Replies 1 ·
Replies
1
Views
2K
Percentage of Electrons Tunneling Through?
  • · Replies 1 ·
Replies
1
Views
2K
Mutilple beam reflection question in Fabry-Perot cavity
  • · Replies 1 ·
Replies
1
Views
3K
Archived How Does an Infinitely High Potential Wall Impact Quantum Wave Functions?
  • · Replies 1 ·
Replies
1
Views
2K
How Does Quantum Tunneling Affect Electron Confinement in Potential Wells?
  • · Replies 9 ·
Replies
9
Views
3K