The Potential Barrier, case: E ≤ V_o - Tunneling

We seek to answer a key question: What happens inside the potential barrier when the energy is less than the potential V. In classical mechanics, the particle cannot exist in this region. In quantum mechanics, it can. Employing mathematics, we explain what happens as attributed to the wave-like behavior of the particle.



Note: Unlike the previous problems, I hope you watch all of the first four of this series, Lec 20 to Lec 23, to fully understand this phenomena.

1. The Free Particle: Continuous States
2. The Free Particle: Analyzing the Solutions
3. The Free Particle: Are Continuous States Physical?
4. The Free Particle: A Gaussian Wave Packet
5. The Free Particle: Calculating Our Wave Packet
6. Solving the Schrödinger Equation
7. Description of Plane Waves
8. Probability Current Density
9. Calculating R and T
10. Explaining Quantum Behavior
11. Particle-like Gets Stopped
12. The Strange Evanescent Wave
13. Infinite Square Well: Deriving Discrete Energy Value
14. Infinite Square Well: What is Zero-Point Energy?
15. Infinite Square Well: Unusual Probability Densities
16. The Scattering Problem
17. Ratio Transmitted Particles
18. Energy Values and Resonance
19. Full Transmission of Part
20. Tunneling: Setting the Situation
21. Tunneling: Deciphering the Wave-like Particle
22. Tunneling: Penetrating the Potential Barrier
23. Tunneling: Further Analysis of T
24. Tunneling: The WKB Approximation Method
25. Introduction
26. Unphysical Solutions
27. Fourier Transform Revisit
28. Outside the Well
29. Anti/Symmetric Solutions
30. Boundary Conditions
31. A Graphical Solution
32. Discrete Energy Specturm

In this course, GMath Physics Instructor Donny Lee gives 32 video lessons on Quantum Mechanics and Physical Problems in One-Dimension.